SU1612315A1 - Device for solving systems of algebraic equations - Google Patents

Abstract

The invention relates to computing and can be used in automatic control systems and technical vision systems. The aim of the invention is to expand the functionality by solving systems of nonlinear algebraic equations. The goal is achieved by the fact that the device contains K counters 1, where K is the order of the algebraic equation system, control block 2, K registers 3 and situation analysis block 4. 3 il.

Description

equations, block 2 controls, K registers 3 and block 4 analysis of situations. -1 il.

WITH "

J

th

(L

Th

U

5 2 The invention relates to computing technology and can be used in control systems and technical vision systems. 5 The aim of the invention is to evaluate the functionality by solving systems of nonlinear equations.

FIG. 1 shows the layout of the device; in fig. 2 is a diagram of performing a situation analysis block for the case of a system of algebraic equations of the form

a, x + az

afh + ag

(one)

in fig. 3 - interpretation of the process of searching for new coordinates of point A (,, Y 1) taking into account its old coordinates

(A, cholesterol.

   The device contains K counters 1, where K is the order of the algebraic equation system, control block 2, register K registers 3, situation analysis block 4, inputs of .5 coefficients and right-hand parts of the device control system, input 6 of the device resolution accuracy and output 7 devices. The situation analysis block 4 contains the first to the fourth multipliers 8–11, the first to the fourth adders 12–15, the first and second calculators 16 and 17, the module, the fifth adder 18, and the comparator 19.

The solutions of the original system of algebraic equations are optimally selected in the field of the definition of unknowns. It is understood that in this specified area of definition, which is known in advance, there is only one solution, and

sought for

Since the operation of the device is given in real time in control systems, the control parameters (they, as a rule, are either a solution of algebraic equation systems or are uniquely associated with it) in practice cannot be shortly - the time interval (adjustment cycle) has changed significantly; Therefore, in the proposed device, the search for a solution of the system of algebraic equations is performed in the vicinity of the solution found in the previous cycle.

The process of finding a satisfactory (with the required accuracy) solution

is removed in FIG. 3. First, the coordinates of point A (the old solution of the system) are checked for satisfaction as a solution (with a given accuracy) of the original system of algebraic equations (1). If the coordinates of the point Y.2 are sufficiently resolved, then the old coordinates X, X are output: J If the coordinates of the indicated point do not satisfy as the solution, then the coordinates of the following points are sequentially checked:

15

AH, (Xc + 1); Ac + 2 (Chl + 1); (YC - 1); AU ,, X (.; (Ye - DJ;

C44 (Xc O; (YC - 1) 1;

Ac., - 1) Ac + vrXs - 1);

(Y (. + 1) J J

ASL xc; (YC +, 1); + 1); (YC + ОЪ Ac + чК е + 2);

/

1) 3.

and so on until the moment of satisfaction of the solution of the coordinates of the indicated points

Thus, the line connecting the listed points is a spiral, i.e. the stale point is checked first, then the gap point of the indicated error value, then the double value of the required error, etc. This ensures prompt (in a probabilistic sense) finding a solution to the system.

After finding a new point Yy ,, whose coordinates satisfy the solution, then

V. - Y Y Y

H. -. Хц, с- Н

And the process starts again.

The described algorithm is implemented by the device as follows.

From the outputs of the counters 1 and from the inputs 5 of the device, the information enters the corresponding inputs of the situation analysis unit 4, where it is checked for compliance of the specified information with the original system of algebraic equations. the single value of the signal is entered and the solution found is written into the re-,

516

gnst 3, and also set to the initial state of the block 2 control

If the proposed solution does not satisfy, then a zero value of the signal is saved at the output of the situation analyzer 4, which allows the control unit 2 to change the contents of counters 1 (the contents of only one of the counters 1 are changed each time) so that the information in the counters changed according to the described algorithm. Then the situation analysis unit 4 checks the solution and the process is repeated anew.

Claims (1)

Invention Formula A device for solving systems of algebraic equations containing registers from first to Kth, where K is the order of the system of algebraic equations, and a control unit, which is so that, in order to extend the functionality by solving systems of nonlinear algebraic equations, it contains 6 first to K-th counters and a situation analysis block, with the outputs from the first to K and the first group of the control unit connected respectively to the inputs of the increment of counters from the first to the K-th; the outputs from the first to K-th second group of the control unit decrement counters from the first to the K-th, exit i-ro counter (where i 1, ..., K) is connected to the i-th information input of the situation analysis block and to the information input of the i-ro register, the output of which is connected to the i-th output of the result device, inputs coefficients and the right parts of the system of equations of the device are connected respectively to the information inputs of the block group analysis of the situation, the input of the solution accuracy value of the device is connected to the (K + 1) -th information input of the situation analysis unit, the output of which is connected to the input of the indication of the presence of the decision of the control unit and to the inputs of the record-read register 1.1 Thebes. 2 Thebes. five