AR051497A1 - DECOMPOSITION OF OWN VALUE AND DECOMPOSITION OF SINGULAR VALUE OF MATRICES USING JACOBI ROTATION - Google Patents
DECOMPOSITION OF OWN VALUE AND DECOMPOSITION OF SINGULAR VALUE OF MATRICES USING JACOBI ROTATIONInfo
- Publication number
- AR051497A1 AR051497A1 ARP050104809A AR051497A1 AR 051497 A1 AR051497 A1 AR 051497A1 AR P050104809 A ARP050104809 A AR P050104809A AR 051497 A1 AR051497 A1 AR 051497A1
- Authority
- AR
- Argentina
- Prior art keywords
- matrix
- decomposition
- matrices
- jacobi rotation
- jacobi
- Prior art date
Links
Classifications
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L25/00—Baseband systems
- H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
- H04L25/0202—Channel estimation
- H04L25/024—Channel estimation channel estimation algorithms
- H04L25/0242—Channel estimation channel estimation algorithms using matrix methods
- H04L25/0248—Eigen-space methods
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/16—Matrix or vector computation, e.g. matrix-matrix or matrix-vector multiplication, matrix factorization
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- General Physics & Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Analysis (AREA)
- Computational Mathematics (AREA)
- Signal Processing (AREA)
- Computer Networks & Wireless Communication (AREA)
- Algebra (AREA)
- General Engineering & Computer Science (AREA)
- Software Systems (AREA)
- Power Engineering (AREA)
- Databases & Information Systems (AREA)
- Computing Systems (AREA)
- Complex Calculations (AREA)
- Radio Transmission System (AREA)
- Image Analysis (AREA)
- Image Processing (AREA)
Abstract
Técnicas para descomponer matrices utilizando la rotacion de Jacobi. Multiples iteraciones de la rotacion de Jacobi se llevan a cabo sobre una primera matriz de valores complejos con multiples matrices de rotacion de Jacobi de valores complejos para llevar a cero los elementos que se encuentran fuera de l diagonal en la primera matriz. Par cada iteracion, se puede formar una submatriz en base a la primera matriz y se puede descomponer para obtener vectores propios para la submatriz, y se puede formar una matriz de rotacion de Jacobi con los vectores propios y se puede utilizar para actualizar la primera matriz. Una segunda matriz de valores complejos, la cual contiene vectores ortogonales, se deriva en base a las matrices de rotacion de Jacobi. Para la descomposicion del valor propio, se puede derivar una tercer matriz de valores propios en base a las matrices de rotacion de Jacobi. Para la descomposicion del valor singular, una cuarta matriz con vectores singulares izquierdos y una matriz e valores singulares se pueden derivar en base a las matrices de rotacion de Jacobi.Techniques for decomposing matrices using Jacobi rotation. Multiple iterations of the Jacobi rotation are carried out on a first matrix of complex values with multiple Jacobi rotation matrices of complex values to zero the elements that are outside the diagonal in the first matrix. For each iteration, a submatrix can be formed based on the first matrix and can be decomposed to obtain proper vectors for the submatrix, and a Jacobi rotation matrix can be formed with the eigenvectors and can be used to update the first matrix . A second matrix of complex values, which contains orthogonal vectors, is derived based on Jacobi rotation matrices. For the decomposition of the eigenvalue, a third matrix of eigenvalues can be derived based on Jacobi's rotation matrices. For the decomposition of the singular value, a fourth matrix with left singular vectors and a matrix and singular values can be derived based on Jacobi rotation matrices.
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US62832404P | 2004-11-15 | 2004-11-15 |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| AR051497A1 true AR051497A1 (en) | 2007-01-17 |
Family
ID=36129731
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| ARP050104809 AR051497A1 (en) | 2004-11-15 | 2005-11-16 | DECOMPOSITION OF OWN VALUE AND DECOMPOSITION OF SINGULAR VALUE OF MATRICES USING JACOBI ROTATION |
Country Status (9)
| Country | Link |
|---|---|
| EP (1) | EP1828923A2 (en) |
| JP (1) | JP4648401B2 (en) |
| KR (2) | KR20090115822A (en) |
| CN (2) | CN101438277A (en) |
| AR (1) | AR051497A1 (en) |
| CA (1) | CA2588176C (en) |
| IN (1) | IN2012DN01928A (en) |
| TW (1) | TWI407320B (en) |
| WO (1) | WO2006053340A2 (en) |
Families Citing this family (28)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US8204149B2 (en) | 2003-12-17 | 2012-06-19 | Qualcomm Incorporated | Spatial spreading in a multi-antenna communication system |
| US7336746B2 (en) | 2004-12-09 | 2008-02-26 | Qualcomm Incorporated | Data transmission with spatial spreading in a MIMO communication system |
| US8923785B2 (en) | 2004-05-07 | 2014-12-30 | Qualcomm Incorporated | Continuous beamforming for a MIMO-OFDM system |
| US8285226B2 (en) | 2004-05-07 | 2012-10-09 | Qualcomm Incorporated | Steering diversity for an OFDM-based multi-antenna communication system |
| US7978649B2 (en) | 2004-07-15 | 2011-07-12 | Qualcomm, Incorporated | Unified MIMO transmission and reception |
| US7602855B2 (en) * | 2005-04-01 | 2009-10-13 | Interdigital Technology Corporation | Method and apparatus for singular value decomposition of a channel matrix |
| US8543070B2 (en) | 2006-04-24 | 2013-09-24 | Qualcomm Incorporated | Reduced complexity beam-steered MIMO OFDM system |
| US8290089B2 (en) * | 2006-05-22 | 2012-10-16 | Qualcomm Incorporated | Derivation and feedback of transmit steering matrix |
| KR101325370B1 (en) | 2006-08-17 | 2013-11-11 | 인텔 코포레이션 | Method and apparatus for providing efficient precoding feedback in a mimo wireless communication system |
| CN101488759B (en) * | 2009-02-24 | 2012-04-11 | 东南大学 | Decoding method for MIMO OFDM system low density correcting code |
| CN101908123B (en) * | 2010-06-01 | 2012-06-27 | 福建新大陆电脑股份有限公司 | Hardware logic implementation device for Hough operation |
| CN102013907B (en) * | 2010-09-29 | 2013-12-11 | 中国科学院声学研究所 | Channel information feedback method of beam shaping system with Mt*2MIMO (Multiple Input Multiple Output) characteristic |
| CN103780330B (en) * | 2012-10-19 | 2017-04-26 | 华为技术有限公司 | Signal transmission method, system and device |
| CN105323037A (en) * | 2014-08-01 | 2016-02-10 | 中国移动通信集团公司 | Pre-coding method and device according to complex matrix |
| CN105323036A (en) * | 2014-08-01 | 2016-02-10 | 中国移动通信集团公司 | Method and device for performing singular value decomposition on complex matrix and computing equipment |
| CN105871503B (en) * | 2015-01-22 | 2019-03-12 | 华邦电子股份有限公司 | Multiple input, multiple output wireless communication system and its channel decomposition method |
| CN104618293B (en) * | 2015-01-27 | 2017-11-28 | 东南大学 | A kind of optimization method of the unitary transformation matrix of smooth singular value decomposition |
| CN104636632B (en) * | 2015-03-10 | 2017-12-15 | 中国人民解放军国防科学技术大学 | The small amount of storage computation of table lookup method of high-precision phase position |
| CN105403865B (en) * | 2015-10-23 | 2017-10-27 | 河海大学 | Multi-carrier signal constant envelope modulation methodology |
| EP3583522A4 (en) * | 2017-02-17 | 2020-12-30 | Kyndi, Inc. | Method and apparatus of machine learning using a network with software agents at the network nodes and then ranking network nodes |
| CN107102841A (en) * | 2017-04-06 | 2017-08-29 | 上海晟矽微电子股份有限公司 | A kind of coordinate transform parallel calculating method and device |
| CN108228536B (en) * | 2018-02-07 | 2021-03-23 | 成都航天通信设备有限责任公司 | Method for realizing Hermitian matrix decomposition by using FPGA (field programmable Gate array) |
| CN110110285B (en) * | 2019-04-10 | 2020-05-22 | 浙江大学 | Parallel Jacobi calculation acceleration implementation method for FPGA |
| CN110531866B (en) * | 2019-10-29 | 2020-03-13 | 深圳市瑞立视多媒体科技有限公司 | Method for performing attitude calculation based on improved inverse kinematics and related equipment |
| CN112015369B (en) * | 2020-08-25 | 2022-09-16 | 湖南艾科诺维科技有限公司 | FPGA-based signal processing method, electronic device and storage medium |
| CN114184837B (en) * | 2021-12-09 | 2022-10-18 | 电子科技大学 | Instantaneous frequency measurement method based on Cordic algorithm |
| CA3239129A1 (en) * | 2021-12-10 | 2023-06-15 | Matthew Brandon ROBINSON | Methods and apparatus for correcting timing and frequency offsets between communications receivers and transmitters |
| CN116382617B (en) * | 2023-06-07 | 2023-08-29 | 之江实验室 | Singular value decomposition accelerator with parallel ordering function based on FPGA |
Family Cites Families (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2976888B2 (en) * | 1996-06-27 | 1999-11-10 | 日本電気株式会社 | Circuit simulation method |
| DE19626984C1 (en) * | 1996-07-04 | 1997-11-27 | Siemens Ag | Process for computer-aided determination of a system context function |
| US6510354B1 (en) * | 1999-04-21 | 2003-01-21 | Ching-Fang Lin | Universal robust filtering process |
| US6859747B2 (en) * | 2001-04-26 | 2005-02-22 | Siemens Energy & Automation, Inc. | Method and apparatus for self-calibrating a motion control system |
| US7327800B2 (en) * | 2002-05-24 | 2008-02-05 | Vecima Networks Inc. | System and method for data detection in wireless communication systems |
-
2005
- 2005-11-15 CA CA2588176A patent/CA2588176C/en not_active Expired - Fee Related
- 2005-11-15 CN CNA2005800464908A patent/CN101438277A/en active Pending
- 2005-11-15 KR KR1020097022241A patent/KR20090115822A/en not_active Application Discontinuation
- 2005-11-15 WO PCT/US2005/041783 patent/WO2006053340A2/en active Application Filing
- 2005-11-15 CN CN2005800464414A patent/CN101390351B/en not_active Expired - Fee Related
- 2005-11-15 JP JP2007541491A patent/JP4648401B2/en not_active Expired - Fee Related
- 2005-11-15 EP EP20050851789 patent/EP1828923A2/en not_active Ceased
- 2005-11-15 KR KR1020077013411A patent/KR101084792B1/en not_active IP Right Cessation
- 2005-11-15 TW TW094139368A patent/TWI407320B/en active
- 2005-11-16 AR ARP050104809 patent/AR051497A1/en unknown
-
2007
- 2007-11-15 IN IN1928DEN2012 patent/IN2012DN01928A/en unknown
Also Published As
| Publication number | Publication date |
|---|---|
| KR101084792B1 (en) | 2011-11-21 |
| KR20070086178A (en) | 2007-08-27 |
| JP2008521294A (en) | 2008-06-19 |
| CN101438277A (en) | 2009-05-20 |
| JP4648401B2 (en) | 2011-03-09 |
| WO2006053340A3 (en) | 2008-07-31 |
| CN101390351B (en) | 2012-10-10 |
| CA2588176C (en) | 2012-10-16 |
| CA2588176A1 (en) | 2006-05-18 |
| KR20090115822A (en) | 2009-11-06 |
| WO2006053340A2 (en) | 2006-05-18 |
| TW200703039A (en) | 2007-01-16 |
| IN2012DN01928A (en) | 2015-07-24 |
| CN101390351A (en) | 2009-03-18 |
| TWI407320B (en) | 2013-09-01 |
| EP1828923A2 (en) | 2007-09-05 |
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Legal Events
| Date | Code | Title | Description |
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| FB | Suspension of granting procedure |