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TW200703039A - Eigenvalue decomposition and singular value decomposition of matrices using jacobi rotation - Google Patents

Eigenvalue decomposition and singular value decomposition of matrices using jacobi rotation

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Publication number
TW200703039A
TW200703039A TW094139368A TW94139368A TW200703039A TW 200703039 A TW200703039 A TW 200703039A TW 094139368 A TW094139368 A TW 094139368A TW 94139368 A TW94139368 A TW 94139368A TW 200703039 A TW200703039 A TW 200703039A
Authority
TW
Taiwan
Prior art keywords
matrix
jacobi rotation
matrices
decomposition
singular value
Prior art date
Application number
TW094139368A
Other languages
Chinese (zh)
Other versions
TWI407320B (en
Inventor
John W Ketchum
Rodney J Walton
Mark S Wallace
Steven J Howard
Hakan Inanoglu
Original Assignee
Qualcomm Inc
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Qualcomm Inc filed Critical Qualcomm Inc
Publication of TW200703039A publication Critical patent/TW200703039A/en
Application granted granted Critical
Publication of TWI407320B publication Critical patent/TWI407320B/en

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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 OR CALCULATING; 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

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  • 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

Techniques for decomposing matrices using Jacobi rotation are described. Multiple iterations of Jacobi rotation are performed on a first matrix of complex values with multiple Jacobi rotation matrices of complex values to zero out the off-diagonal elements in the first matrix. For each iteration, a submatrix may be formed based on the first matrix and decomposed to obtain eigenvectors for the submatrix, and a Jacobi rotation matrix may be formed with the eigenvectors and used to update the first matrix. A second matrix of complex values, which contains orthogonal vectors, is derived based on the Jacobi rotation matrices. For eigenvalue decomposition, a third matrix of eigenvalues may be derived based on the Jacobi rotation matrices. For singular value decomposition, a fourth matrix with left singular vectors and a matrix of singular values may be derived based on the Jacobi rotation matrices.
TW094139368A 2004-11-15 2005-11-15 Apparatus and method for decomposing matrices using jacobi rotation TWI407320B (en)

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
US62832404P 2004-11-15 2004-11-15

Publications (2)

Publication Number Publication Date
TW200703039A true TW200703039A (en) 2007-01-16
TWI407320B TWI407320B (en) 2013-09-01

Family

ID=36129731

Family Applications (1)

Application Number Title Priority Date Filing Date
TW094139368A TWI407320B (en) 2004-11-15 2005-11-15 Apparatus and method for decomposing matrices using jacobi rotation

Country Status (9)

Country Link
EP (1) EP1828923A2 (en)
JP (1) JP4648401B2 (en)
KR (2) KR101084792B1 (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)

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* Cited by examiner, † Cited by third party
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
WO2008021396A2 (en) 2006-08-17 2008-02-21 Interdigital Technology Corporation 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 A Channel Information Feedback Method for Mt×2 MIMO Eigenbeamforming System
CN103780330B (en) 2012-10-19 2017-04-26 华为技术有限公司 Signal transmission method, system and device
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
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
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 channel decomposition method thereof
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
AU2018220752A1 (en) * 2017-02-17 2019-08-29 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
US12387103B2 (en) * 2021-05-12 2025-08-12 Microsoft Technology Licensing, Llc Backpropagation using parametrizing angles of unitary matrix
CN114184837B (en) * 2021-12-09 2022-10-18 电子科技大学 An Instantaneous Frequency Measurement Method Based on Cordic Algorithm
CN118476193A (en) 2021-12-10 2024-08-09 拉姆帕特通信股份有限公司 Method and apparatus for correcting timing and frequency offsets between a communications receiver and transmitter
CN116539035B (en) * 2022-01-26 2025-09-02 舜宇光学（浙江）研究院有限公司 Pose matrix determination method, positioning method, processor and mobile robot
CN115659880B (en) * 2022-09-01 2025-08-12 南京模数智芯微电子科技有限公司 Hardware circuit and method of principal component analysis algorithm based on singular value decomposition
CN116382617B (en) * 2023-06-07 2023-08-29 之江实验室 Singular value decomposition accelerator with parallel ordering function based on FPGA

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US7327800B2 (en) * 2002-05-24 2008-02-05 Vecima Networks Inc. System and method for data detection in wireless communication systems

Also Published As

Publication number Publication date
JP2008521294A (en) 2008-06-19
CN101390351A (en) 2009-03-18
WO2006053340A2 (en) 2006-05-18
CN101438277A (en) 2009-05-20
CN101390351B (en) 2012-10-10
WO2006053340A3 (en) 2008-07-31
KR20090115822A (en) 2009-11-06
EP1828923A2 (en) 2007-09-05
JP4648401B2 (en) 2011-03-09
AR051497A1 (en) 2007-01-17
CA2588176A1 (en) 2006-05-18
KR20070086178A (en) 2007-08-27
CA2588176C (en) 2012-10-16
IN2012DN01928A (en) 2015-07-24
TWI407320B (en) 2013-09-01
KR101084792B1 (en) 2011-11-21

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