| 求块-Toeplitz矩阵QR分解中R的一种快速算法 |
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| 引用本文： | 刘俊,胡艳军.求块-Toeplitz矩阵QR分解中R的一种快速算法[J].安徽大学学报(自然科学版),2009,33(4). |
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| 作者姓名： | 刘俊 胡艳军 |
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| 作者单位： | 安徽大学,计算智能与信号处理教育部重点实验室,电子科学与技术学院,安徽,合肥,230039 |
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| 基金项目： | 国家自然科学基金资助项目(60772123) |
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| 摘 要： | 在前人研究的基础上,对块数为m×n、阶数为m r×ns的块-Toep litz矩阵T提出利用推广的Schur算法,通过对TTT的位移结构表示并结合Hyperbolic Householder变换对生成子矩阵作用,得到QR分解中上三角矩阵R的一种快速算法.在工程应用中采用一定近似,计算量可以达到O(ns3),较传统的Schur算法的计算量大大减小.
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| 关 键 词： | 块-Toeplitz矩阵 QR分解 Schur算法 HyperbolicHouseholder变换 |
Fast algorithm for R of QR decomposition of block-Toeplitz matrices |
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| LIU Jun,HU Yan-jun.Fast algorithm for R of QR decomposition of block-Toeplitz matrices[J].Journal of Anhui University(Natural Sciences),2009,33(4). |
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| Authors: | LIU Jun HU Yan-jun |
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| Institution: | Key Laboratory of Intelligent Computing and Signal Processing;Ministry of Education;School of Electronic Science and Technology;Anhui University;Hefei 230039;China |
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| Abstract: | In the paper,on the basis of their predecessors,a fast algorithm for the upper triangular matrix R of QR decomposition of T( which was m × n block-Toeplitz matrix with r × s rectangular blocks) using only O( ns~3 )multiplication was presented,where we got R by computing displacement structure of T~TT,and used the Schur algorithm and combined with Hyperbolic Householder transformation. Compared with the traditional method of Schur algorithm,we greatly reduced the amount of computation. |
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| Keywords: | block-Toeplitz matrix QR decomposition Schur algorithm Hyperbolic Householder transformation |
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