Fast algorithm for Moore-Penrose inverse of Toeplitz-type matrices

doi:10.3778/j.issn.1002-8331.2010.30.001

Computer Engineering and Applications ›› 2010, Vol. 46 ›› Issue (30): 1-4.DOI: 10.3778/j.issn.1002-8331.2010.30.001

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Fast algorithm for Moore-Penrose inverse of Toeplitz-type matrices

AN Xiao-hong，XU Zhong，LU Quan，WANG Shu-xun

College of Science，Northwestern Polytechnical University，Xi’an 710072，China

Received:2010-05-10 Revised:2010-09-06 Online:2010-10-21 Published:2010-10-21
Contact: AN Xiao-hong

行满秩Toeplitz型矩阵Moore-Penrose逆的快速算法

安晓虹，徐仲，陆全，王树勋

西北工业大学理学院，西安 710072

通讯作者: 安晓虹

Abstract

Abstract: A new fast algorithm for Moore-Penrose inverse of Toeplitz-type matrices with full row rank is presented by forming a symmetric block matrix.The computational complexity of this algorithm is O（mn）+O（m²），while solving T⁺ from TT（TT^T）^-1 needs O（m2n）+O（m³）.Examples show the efficiency of the fast algorithm.

Key words: Toeplitz-type matrix, Moore-Penrose inverse, symmetric, fast algorithm

摘要： 通过构造对称分块矩阵给出了秩为m的m×n阶Toeplitz型矩阵Moore-Penrose逆的快速算法。该算法计算复杂度为O（mn）+O（m²），而由T^T（TT^T）^-1直接求解所需运算量为O（m²n）+O（m3）。数值算例表明了该快速算法的有效性。

关键词: 06Toeplitz型矩阵, Moore-Penrose逆, 对称化, 快速算法

CLC Number:

TP301.6

AN Xiao-hong，XU Zhong，LU Quan，WANG Shu-xun. Fast algorithm for Moore-Penrose inverse of Toeplitz-type matrices[J]. Computer Engineering and Applications, 2010, 46(30): 1-4.

安晓虹，徐仲，陆全，王树勋. 行满秩Toeplitz型矩阵Moore-Penrose逆的快速算法[J]. 计算机工程与应用, 2010, 46(30): 1-4.

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Fast algorithm for Moore-Penrose inverse of Toeplitz-type matrices

行满秩Toeplitz型矩阵Moore-Penrose逆的快速算法

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