JP2003150565A - Computer - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a computer capable of enhancing the possibility of determining the solution at a high speed by a simple control when executing a repetitive solution. SOLUTION: This computer outputs a result by executing arithmetic processing by the repetitive solution in a control part 103 on the basis of an inputted expression, an initial value of a variable in the expression, and a solution existing range, and has a memory 105 for respectively storing the lower limit and the upper limit of the solution existing range. The control part 103 is realized by executing the control for determining the size of Xn+1 and Xn when calculating a halfway result Xn+1 of (n+1) order from a halfway result Xn of n order of the arithmetic processing by the repetitive solution, removing a range smaller than the Xn from the solution existing range by storing the Xn in the lower limit memory when the Xn+1 is larger than the Xn, removing a range larger than the Xn from the solution existing range by storing the Xn in the upper limit memory when the Xn+1 is smaller than the Xn, making a calculation of (n+2) order when the Xn+1 falls within the solution existing range, and finishing the calculation when the Xn+1 falls outside the solution existing range.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a calculator (electronic desk calculator), scientific calculator, pocket computer, and other calculators, and more particularly, to a target value by an iterative solution method from an expression input by an operator and initial values. The present invention relates to a computing device to be obtained.

[0002]

2. Description of the Related Art Generally, in an iterative solution method such as Newton's method or steepest descent method, when a solution, a maximum value, a minimum value, etc. (hereinafter simply referred to as "solution") is obtained from a certain expression, an initial value X is used.
The next X1 is obtained from 0, the next X1 is obtained from X2, and the like. Iterative calculation is performed, and after finally performing several calculations, the finally obtained value is obtained. At this time, a solution may or may not be obtained depending on the initial value. However, the initial value for which the solution is obtained depends on the formula, and in general, the initial value cannot be set.

Therefore, in a conventional calculator including a calculator and a scientific calculator, the iterative solution method is executed as shown in FIG.

First, the operator inputs an equation to be calculated (S201), and the initial values of the variables in the above equation and, if necessary, a range in which a solution exists (hereinafter referred to as "solution existence range"). Is input (S202). Next, actual calculation processing is performed from the input expression and the initial value (S20
3) When the solution is obtained, the numerical value of the calculation result is displayed, and when there is an error, an error message is displayed (S204).

The above calculation process (S203) is performed in the procedure shown in FIG.

First, various work areas for arithmetic processing are initialized (S211). Next, when the iterative solution process fails, the number of times (loop number) for resetting the initial value to the counter KAISU is set (S212). For example, the number of loops is 9. Next, iterative solution processing is performed (S213). Specifically, as shown in FIG. 10, first, various work areas in the iterative solution processing are initialized (S221), and the maximum number of trials (loop count) of the iterative solution is entered in the counter count (S222). ). Next, the next X is actually calculated from the input X (S223).

For example, in the Newton method, X = X−f (X) / f ′ (X) (1) (where f (X) is an expression input by the operator, f ′ (X)
Is a value obtained by substituting X into an expression obtained by differentiating f (x). ) Is calculated.

If any error occurs in this calculation (S
224), the iterative solution processing ends. If there is no error and the value of equation (1) (new X) is calculated, it is determined whether or not the solution is reached (S225), and if the solution is reached, the process ends. On the other hand, if the solution is not reached, co
The value of unt is decremented by 1, the process returns to S223, and the processes of S223 to S226 are repeated until the solution is reached or the value of count becomes zero (the loop count set in S222 ends).

Next, as shown in FIG. 9, in this series of iterative solution processing (S213), it is judged whether or not a calculation error has occurred (S214). When an arithmetic error does not occur and a solution can be calculated correctly, or when a grammatical error (syntax error) occurs in the expression itself, this arithmetic processing is terminated as it is. Otherwise, if a calculation error occurs, 1 is subtracted from the value of KAISU, and if the value of KAISU becomes zero (the loop count set in S212 ends), the process ends (S215). If the value of KAISU is not zero, a new initial value is created within the solution existence range (S216). Specifically, as shown in FIG. 11, the upper limit of the solution existence range input by the operator is set to R. HANI, the lower limit is L. HANI, and X is a place to put a new initial value. HANI and L.A. 8 with HANI
The equally divided value is entered (S231). Next, the counter Ac
Put (9-KAISU) in c. That is, every time an initial value is created, 0, 1, 2, ... Next, the initial value (L.HANI + X * Acc) is calculated and put in X (S233). As a result, FIG.
As shown in FIG. HANI to R.I. Up to HANI, initial values are sequentially obtained from the left side (smaller side), and the processes of S213 to S216 are repeated until the value of KAISU becomes zero. Then, as described above, if the solution is found midway, the value is displayed, and if the solution cannot be found by any means, an error is displayed (S204 in FIG. 8).

FIG. 12 shows a display example when the Newton's method is executed on the scientific calculator.

As shown in FIG. 3A, when the application is started, "EQUATION?" Is displayed and the operator is prompted to enter a formula. If the operator uses the formula X2
When -2 = 0 is input and zero is input as the initial value of the variable X in the formula, the values are displayed as shown in FIGS. If necessary, a screen for inputting the solution existence range is displayed as shown in FIG.
Enter. In this example, a = -1 × 10 10, b = 1 ×
It is 10 10. The calculation process is executed to display the result X = 1.4142135 as shown in FIG. Here, the values of the left side L and the right side R of the equation are simultaneously displayed to indicate to the operator whether or not a solution has been reached.

[0012]

However, the above-mentioned technique still has the following problems.

For example, when considering to find X such that (X-2) 2 + 10 = 0 in an application that finds the solution of an equation by the Newton method, there is no real number solution in this equation, so the Newton method is executed a predetermined number of times. However, no solution is obtained, and the calculation is eventually terminated. However, considering the progress of the calculation, it is only going back and forth around the same value, and there is a problem that it takes unnecessary time.

For example, in the case of considering X for which logX = 0 in an application for solving the equation by Newton's method, the value of the expression is defined only in the range of X> 0 in logX. A calculation error occurs if the elapsed time falls within the range of X ≦ 0 even once. Here, when the solution existing range is divided into eight equal parts and the initial value is sequentially given from the left side (smaller side) as in the conventional case, the solution existing range is -10 to
If it is set to 10, the initial value for the first to fifth times is -10,
An error occurs at -7.5, -5, -2.5, 0, and the solution is finally obtained at the sixth initial value of 2.5. In other words, if an error occurs when a certain initial value is given, values similar to the initial value are likely to cause similar errors, but conventionally, the initial value was sequentially set from the left (or right) within the solution existence range. Since it is given, there is a problem that the calculation time becomes long once an error occurs.

Further, if an error occurs once during the calculation, the error processing is performed by displaying an error, or
It is limited to performing iterative solution processing with another initial value. For this reason, it may not be possible to assist the subsequent setting of the initial value, and eventually the solution may not be obtained.

The present invention has been made to solve the above problems, and an object thereof is to obtain a solution at high speed with simple control when executing an iterative solution method. An object of the present invention is to provide a computing device that can continue arithmetic processing even if an error occurs once and increase the possibility of finding a solution.

[0017]

In order to achieve the above-mentioned object of the present invention, the present invention provides a control unit based on an input expression, an initial value of a variable in the expression, and a solution existence range. A computing device that performs an arithmetic process by the iterative solution method and outputs a numerical value of a calculation result when a solution is reached, and an error message when an error occurs, wherein the control unit controls the first and second arithmetic processes by the iterative solution method. As the initial value, one or the other of the lower limit value and the upper limit value of the solution existence range is sequentially adopted, and 2 m divisions (m = 1, 1) within the solution existence range as the third and subsequent initial values.
2, ...) Among the values of the points obtained by performing the control in such a manner that the division order m is the lowest, and the value that is most distant from the initial value immediately before in the order m is adopted. Is.

Further, according to the present invention, based on the input expression, the initial value of the variable in the expression, and the solution existence range, the control unit performs the arithmetic processing by the iterative solution method, and when the solution is reached, A numerical value of the calculation result, and an error message output device when an error occurs. The calculation device stores the values of the (n-1) th intermediate result Xn-1 and the nth intermediate result Xn of the arithmetic processing by the iterative solution method. If a calculation error occurs in the middle of calculation of the (n + 1) th intermediate result Xn + 1, the control unit is provided with the second and first memories The control is such that the midpoint between Xn-1 and Xn is obtained as a new Xn, and Xn + 1 is calculated again based on the value of this Xn.

[0019]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of a computer according to the present invention will be described below with reference to the drawings.

FIG. 1 shows the appearance of a computer according to the present invention.

This device has a liquid crystal display element (LC
D) display unit 101 and key unit 1 as an input unit
It is equipped with 02. The key unit 102 includes [0], [1],
[2], [3], [4], [5], [6], [7],
[8], [9] [. ] [(-)] For inputting numerical values, [x] [÷] [+] [-] for calculating four arithmetic keys, [a] to [z] for alphabet input, [ENTR] has a key for registration and calculation execution. In addition, three keys are specifically provided to implement the features of the present invention. They are [SOLVE
The [R] key is a key for starting execution of the iterative solution method, and [S
The [OLVE] key is a key for executing an operation, and [RAN]
The [GE] key represents each key for displaying a screen for entering the solution existence range.

As shown in FIG. 2, a display unit 101 as a display unit, a key unit 102 as an input unit, and the display unit 101 and the key unit 102 are provided inside the apparatus.
CPU (Central Processing Unit) 103 as a control unit (control means) connected to, a ROM (Read Only Memory) 104, and a RAM (Random Access Memory)
105 is provided. The CPU 103 uses the key unit 10
In response to the input from 2 (key input), the process described below is executed, and control is performed to display the calculation, input information, and the calculation result on the display unit 101. Further, the ROM 104 stores a control program for performing key input, calculation, execution of display of input information and calculation result, and control, various constant data, a character generator for display, and the like. Also, R
The AM 105 is composed of a display area (display RAM), a work area (work area), and other data storage areas. In these areas, key input, calculation, input information and calculation are performed. Various kinds of information for executing and controlling the display of results, numerical values and mathematical expressions input by the operator are stored, and values and results in the middle of the calculation are also stored.

The computer of the present invention shown in FIG. 1 performs the same operation as shown in FIG. 8 as a whole when executing the iterative solution method.

That is, the operator first inputs an equation to be calculated (S201), and also inputs the initial value of the variable in the above equation and, if necessary, the solution existence range (S20).
2). Next, actual calculation processing is performed from the input expression and the initial value (S203), and when the solution is obtained, the numerical value of the calculation result is displayed, and when an error occurs, an error message or the like is displayed (S2).
04).

Based on this premise, this computing apparatus has three improvements, which are described below, in addition to the conventional processing.

The first improvement is a modification of the iterative solution execution process (S213; details are shown in FIG. 10) of the arithmetic processes shown in FIG. The second improvement is a modification of the initial value creation processing (S216, which is shown in detail in FIG. 11) of the arithmetic processing shown in FIG. The third improvement is that the flow itself of the arithmetic processing of FIG. 9 is changed and the execution processing of the iterative solution method is changed.

First, the first improvement will be described. Here, instead of the conventional iterative solution processing (FIG. 10), the following iterative solution processing is performed.

It should be noted that the work area in the RAM 105 shown in FIG. KEIKA,
As a lower limit memory, L. KEIKA is set. Also, oldX (the previous X) is provided as the first memory.

As shown in FIG. 3, first, various work areas are initialized in the iterative solution processing (S101).
Before entering the loop, R.I.
KEIKA, L .; Initialize KEIKA. Since no calculation has been made at first, the positive and negative limits of the variable to be obtained are input (S102). In addition, the maximum number of trials (loop count) of the iterative solution method is counted by the counter cou.
nt (S103). Then the current X in oldX
Is stored (S104). This is the step S10 described later.
This is for comparing the magnitude of the new intermediate result X and the immediately preceding intermediate result X at 8. Next, from the actual input X to the next X
Is calculated (S105).

For example, in the Newton method, X = X−f (X) / f ′ (X) ... (2) (where f (X) is an expression input by the operator, f ′ (X)
Is a value obtained by substituting X into an expression obtained by differentiating f (X). ) Is calculated.

If any error occurs in this calculation (S
106), and this iterative solution processing ends. If there is no error and the value of equation (2) (new X) is calculated, it is determined whether or not the solution is reached (S107), and if the solution is reached, the process ends.

On the other hand, if the solution has not been reached, it is checked whether the new X has proceeded to the right or left with respect to oldX (the previous X) (S108). If X is moving to the left with respect to oldX (X <oldX), R.X. KE
IKA is set to oldX (S109). Subsequently, X is R. KEIKA value and L.K. It is checked whether or not the solution existing range determined by the value of KEIKA is popped out. X
Is proceeding to the left, X is L. KEIKA
(S110). On the contrary, when X is proceeding to the right with respect to oldX (X> oldX), L.L. KEIKA
To oldX (S111). Subsequently, X is R. KE
IKA value and L.I. It is checked whether or not the solution existing range determined by the value of KEIKA is popped out. Since X is moving to the right, X is set to R.R. It is compared with KEIKA (S112). In S110 and S112 above, X
R. KEIKA value and L.K. If it is outside the solution existence range defined by the value of KEIKA, this iterative solution processing ends.

On the other hand, when X is R. KEIKA value and L.K. If it is within the solution existence range determined by the value of KEIKA, it is determined whether the value of count has become zero (the number of loops set in S222 ends) by subtracting 1 from the value of count (S113). . If the value of count is zero, this iterative solution processing is terminated, while
If the value of count is not zero, the solution is obtained or the intermediate results jump out of the solution existence range S104 to S104.
The processing of 113 is repeated.

As described above, the solution existence range is defined based on the range in which the intermediate result Xn moves, and when the intermediate result Xn goes out of the solution existing range, the search for the solution is terminated at that stage, which is wasteful. It is possible to avoid spending time and perform arithmetic processing at high speed.

Next, the second improvement will be described. Here, instead of the conventional initial value creation processing (FIG. 11), the following initial value creation processing is performed. As shown in FIG. 9, the value of the counter KAISU is sequentially decreased to 9, 8, 7, ... 2, 1 every time this initial value creation process is called.

The lower limit (left end) of the solution existence range input by the operator is L. HANI, the upper limit (far right) to R.I. HANI, and X is a place to put a new initial value.

As shown in FIG. 4, first, the counter KAI
Check the value of SU (S121), KAISU = 9
In the case of (first call), the L. The value of HANI (far left) is set as the initial value X (S122). In addition, KAISU =
8 (second call), R. HANI (far right)
Is set as the initial value X (S123, S124). KAI
When the value of SU is neither 9 nor 8, R.I. HANI value and L.H. A value obtained by dividing the difference from the value of HANI into eight equal parts is put into X (S125). Next, a branch is made according to the value of KAISU (S126). That is, when KAISU = 7,
The counter Acc is set to 4 (S129), and (L.
The value of HANI + X * Acc) is set as the initial value X (S13).
0). At this time, since Acc = 4, the initial value X is L.L. HANI (far left) and R.I. It becomes a bisector between HANI (far right). Also, the value of KAISU is 5 in S126.
Or, in case of 6, Acc (26-KAISU * 4)
Is set (S128), and similarly (L.HANI + X
The value of * Acc) is set as the initial value X (S130). At this time, the above L. HANI, R .; The quadrant between the HANI and the bisector becomes the initial value X. Also, K in S126
When the value of AISU is 1, ..., 4, A
cc is set to (9-KAISU * 2), and the value of (L.HANI + X * Acc) is similarly set as the initial value X (S130). At this time, R. HANI and L.A. HANI
The eight equal points between and are the initial value X.

In this case, as shown in FIG. 7B, it is possible to adopt the initial value that is the farthest from the initial value that has been adopted in the past within the solution existence range. Therefore, it can be expected that the solution can be obtained with a shorter number of times of execution than the conventional method.

For example, in an application for obtaining the solution of an equation by the Newton method, when it is considered to obtain X such that logX = 0, after an error occurs at an initial value of -10, 10 is adopted as the next initial value. It As a result,
The solution is obtained with the second initial value. Therefore, the solution can be obtained with a shorter number of times of execution than the conventional example (6 times) described above.

Next, the third improvement will be described. Here, instead of the conventional arithmetic processing (FIG. 9) and the iterative solution processing included therein (FIG. 10), the following arithmetic processing and iterative solution processing included therein are performed.

In the work area in the RAM 105 shown in FIG. 2, FIRST. flag
Is newly established. In addition, a second memory oldX2 is newly provided to store the intermediate result of the calculation.

This arithmetic processing is performed in the procedure as shown in FIG.

As shown in FIG. 5, first, various work areas for arithmetic processing are initialized (S131). Next, when the iterative solution processing fails, the counter KAI
The number of times (loop number) 9 for resetting the initial value to SU is set (S132). Next, FIRST. 1 is set as the initial setting of the flag. Next, iterative solution processing is performed (S
134). Specifically, as shown in FIG. 6, first, various work areas are initialized in the iterative solution processing (S
141), the maximum number of trials (loop count) of the iterative solution method is put into the counter count (S142). Then ol
After storing the current value of X in dX (S143),
The next X is actually calculated from the current X (S144).

For example, X = X−f (X) / f ′ (X) (2), which is the same equation as the above Newton's method (where f (X) is an equation input by the operator, f ′ ( X)
Is a value obtained by substituting X into an expression obtained by differentiating f (X). ) Is calculated.

If any error occurs in this calculation (S
145), the iterative solution processing ends. If there is no error and the value of equation (2) (new X) is calculated, it is determined whether or not the solution is reached (S146), and if the solution is reached, the process ends.

On the other hand, if the solution has not been reached, FIRST. fl
0 is put in ag (S147). Also, for oldX2,
The value of oldX (the value of X immediately before at this point) is entered and saved (S148). Subtract 1 from the value of count, return to S143, and repeat the processing of S143 to S149 until a solution is reached or the value of count becomes zero (the loop count set in S142 ends).

Next, as shown in FIG. 5, in this series of iterative solution processing (S134), it is judged whether or not a calculation error has occurred (S135). When an arithmetic error does not occur and a solution can be calculated correctly, or when a grammatical error (syntax error) occurs in the expression itself, this arithmetic processing is terminated as it is. Otherwise, if a calculation error occurs, 1 is subtracted from the value of KAISU, and if the value of KAISU becomes zero (the number of loops set in S132 ends), the process ends (S136).

If the value of KAISU is not zero in S136, FIRST. Whether or not flag = 0, that is, calculation for obtaining X even once in the past (S144 in FIG. 6)
Is executed correctly. At the same time, it is determined whether or not the error occurred when f (X) was calculated (S137). This is to know that X, which was at a position where f (X) can be calculated at least once, has entered a region where it cannot be calculated. FIRST. fl
ag ≠ 0, or an error occurred in f
If it is not time to calculate (X), a new initial value is created within the solution existence range set by the operator (S138). In addition,
The initial value creation processing according to the second improvement described above may be adopted.

On the other hand, in S137, FIRST. flag =
If it is 0 and an error has occurred during the calculation of f (X), (oldX + oldX2) / 2 is put into X (S139). At this time, oldX contains the value Xn when the error occurred, and oldX2 contains the value Xn-1 immediately before the oldX. So these old
The value of the midpoint of X, oldX2 is obtained and set as the new value of X. Then, returning to S134, the same iterative solution method is calculated again. When the value of the midpoint between Xn-1 and Xn results in the same error, oldX2 holds Xn-1 throughout the error. The value of the middle point is reset only for oldX. Therefore, until there is no error, o
The value of ldX approaches the value of oldX2. When no calculation error occurs and the solution can be calculated correctly, the calculation process ends (S135).

In this way, even if an error occurs once in an undefined area, the iterative solution method can be continued, and therefore the possibility of finding a solution can be increased as compared with the conventional method. Also, a solution can be obtained from a wider range of initial values.

When an error occurs in the first calculation (S134), Xn-1 does not exist and oldX2 is indefinite. Therefore, the calculation (S139) for obtaining the midpoint between Xn-1 and Xn cannot be performed. At this time, the process proceeds to S138 to recreate the initial value.

As described above, the features of the improvement of the computer according to the present invention are the following three (1), (2) and (3).

(1) X0, X1, X2 in the iterative solution method
If the graph of the equation is smooth, it is expected that X1 is closer to X1 than X0 and X2 is closer to X1 than X1.

For example, the next X1 is calculated from X0 and X0 is obtained.
When it comes to the right side (larger side), it is expected that the position of the solution currently sought will be on the right side of X0. Conversely, when the intermediate result Xn of the calculation comes to the left (smaller side) of X0 and the next Xn + 1 comes to the right, it often goes back and forth around the same point. It is likely that the true solution will not be reached even if continued.

Therefore, in the computer incorporating the first improvement, the solution existence range is limited based on the intermediate result Xn of the calculation, and when the next intermediate result Xn + 1 is out of the limited solution existence range, At that point, the search for the solution is terminated. Specifically, the lower limit memory L. K
EIKA, upper memory R. KEIKA is provided, and a defined range of numerical values is given as an initial setting. When Xn + 1 is calculated from Xn in the process of finding a solution, Xn + 1 is Xn
If it is on the right side, the left side of Xn is excluded from the solution existence range, and if Xn + 1 is the left side of Xn, the right side of Xn is excluded from the solution existence range. And Xn
If +1 goes out of this range, the calculation is aborted. This allows
It avoids wasting time and operates faster.

It should be noted that the idea that once the user goes back and forth around the same area, the true solution will not be reached even if the calculation is continued, is not mathematically correct. There are any number of expressions that can be solved if the calculation is continued without stopping. However, empirically, it can be said that most general expressions move back and forth once and then back and forth without reaching a solution. This refinement incorporates such heuristics into the actual processing.

(2) In the computer incorporating the second improvement, when the initial value is created from the solution existence range input by the operator, it is located at the farthest position from the previously adopted initial value within the solution existence range. Use the existing initial value. That is, of the values of the points obtained by dividing 2m (m = 1, 2, ...) Within the solution existence range, the division order m is in descending order, and the previous initial value is within the order m. The value farthest from is used. As a result, it is more likely that a solution will be obtained with a shorter number of executions than in the past.

For example, as illustrated in FIG. 7B, the solution existence range input by the operator is L. HANI, R .; HA
It is assumed that NI is set as a lower limit and an upper limit.

First, L. HANI and R.A. HANI is sequentially given as an initial value (note that the numbers in the figure indicate the order of being adopted as an initial value). Next, L. HANI
(Far left) and R. The value of the bisector between HANI (right end) is given as an initial value. Next, L. HANI and R.A. HAN
A point that is a quadrant between I and I and is not a bisector (L.
HANI, R .; The values of points between HANI and the above-mentioned bisecting points) are sequentially given as initial values. Next, L. HANI and R.A. The values of points that are equal to 8 and that are not equal to or equal to 4 points of HANI are similarly given. When calculating the initial value, the number of division points is determined based on the number of times the initial value is stored in the counter.

(3) Even if an error occurs during the calculation of the iterative solution method and it becomes impossible to continue the calculation, the value of the intermediate result before the error occurs depending on the type of the error and the position where the error occurs. The solution may be reached by referring to.

Specifically, the second and first memories are provided for storing the values of the (n-1) th intermediate result Xn-1 and the nth intermediate result Xn of the arithmetic processing by the iterative solution method.

Consider, for example, the case where the solution of the expression f (X) is obtained. After repeating the calculation several times, the intermediate result X
While calculating the next Xn + 1 for n, that is, f (X
Suppose an error occurred during the calculation of n). The value of f (Xn-1) could be calculated, and an error occurred at f (Xn) even though the solution was approaching, so it is possible that the position of the solution was skipped and the error occurred. High, therefore X
It is considered that there is a high possibility that a solution exists by examining between n-1 and Xn. But to find out between Xn-1 and Xn,
A method different from the iterative solution method that led to it is needed.

Therefore, in the computer incorporating the third improvement, a memory area for storing the values of Xn-1 and Xn is provided, and when an error occurs, the area between Xn-1 and Xn is checked. When there is a high possibility that a solution exists, the second and first memories are referred to and the calculation is performed again, and the midpoint between Xn-1 and Xn is set to Xn. Then, the calculation is repeated until the next Xn + 1 can be calculated. As a result, the iterative solution method is continued even if an error is entered once in an undefined area. Therefore,
There is a higher possibility that a solution will be required than in the past. Also,
The solution can be obtained from a wider range of initial values.

The contents of the above-described embodiments are not limited to the above contents unless the gist of the present invention is changed.

[0065]

As described above, according to the present invention, it is possible to obtain a solution with a shorter number of times of execution as compared with the conventional computer.

Further, according to the present invention, it is possible to increase the possibility of obtaining a solution and to obtain a solution from a wider range of initial values, as compared with the conventional computing device.

[Brief description of drawings]

FIG. 1 is a diagram showing an external appearance of a computer according to the present invention.

FIG. 2 is a diagram showing a hardware configuration of the computer according to the present invention.

FIG. 3 is a diagram showing an operation flow of the computer of the present invention.

FIG. 4 is a diagram showing an operation flow of the computer of the present invention.

FIG. 5 is a diagram showing an operation flow of the computer of the present invention.

FIG. 6 is a diagram showing an operation flow of the computer of the present invention.

FIG. 7 is a diagram for explaining the order of setting the initial values of the computer of the present invention and the conventional computer.

FIG. 8 is a diagram showing an operation flow of a conventional computing device and the computing device of the present invention.

FIG. 9 is a diagram showing an operation flow of a conventional computing device.

FIG. 10 is a diagram showing an operation flow of a conventional computing device.

FIG. 11 is a diagram showing an operation flow of a conventional computing device.

FIG. 12 is a diagram showing a display example of a conventional and the above-described computer of the present invention.

[Explanation of symbols]

101 display 102 Input section 103 CPU 104 ROM 105 RAM

Claims (2)

[Claims] 1. A control unit performs arithmetic processing by an iterative solution method based on an input expression, initial values of variables in the expression, and a solution existence range, and when a solution is reached, a numerical value of a calculation result is obtained. In the calculation device that outputs an error message when an error occurs, the control unit sets one or the other of the lower limit value and the upper limit value of the solution existence range as the first and second initial values of the calculation process by the iterative solution method. Among the values of the points obtained by dividing 2m (m = 1, 2, ...) In the solution existence range as an initial value for the third and subsequent times, in order from the lowest division order m, and A computing device, which performs control to adopt a value that is most distant from an initial value immediately before within the order m. 2. The numerical value of the calculation result when a solution is reached by a control unit performing arithmetic processing by an iterative solution method based on an input expression, initial values of variables in the expression, and a solution existence range. , A calculation device which outputs an error message at the time of error, and (n-1) next intermediate result Xn- of the arithmetic processing by the iterative solution method.
The second and the first memories for storing the values of the intermediate results Xn of the 1st and nth order are provided, and the control unit is configured to calculate the intermediate result Xn + 1 of the (n + 1) th order when an operation error occurs. , The second and first memories are referred to, the midpoint between Xn-1 and Xn is obtained as a new Xn, and control is performed to calculate Xn + 1 again based on the value of Xn. And computing device.