Least squares solution of matrix equation AX B* + CY D* = E*

Sang Yeun Shim; Yu Chen

doi:10.1137/S0895479802401059

Least squares solution of matrix equation AX B* + CY D* = E*

Sang Yeun Shim, Yu Chen

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We present an efficient algorithm for the least squares solution (X, Y) of the matrix equation AX B* + CY D* = E with arbitrary coefficient matrices A, B, C, D and the right-hand side E. This method determines the least squares solution (X, Y) with the least norm. It relies on the SVD and generalized SVD of the coefficient matrices and has complexity proportional to the cost of these SVDs.

Original language	English (US)
Pages (from-to)	802-808
Number of pages	7
Journal	SIAM Journal on Matrix Analysis and Applications
Volume	24
Issue number	3
DOIs	https://doi.org/10.1137/S0895479802401059
State	Published - 2003

Keywords

Least norm solution
Matrix equation
Singular value decomposition

ASJC Scopus subject areas

Analysis

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abstract = "We present an efficient algorithm for the least squares solution (X, Y) of the matrix equation AX B* + CY D* = E with arbitrary coefficient matrices A, B, C, D and the right-hand side E. This method determines the least squares solution (X, Y) with the least norm. It relies on the SVD and generalized SVD of the coefficient matrices and has complexity proportional to the cost of these SVDs.",

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AU - Chen, Yu

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AB - We present an efficient algorithm for the least squares solution (X, Y) of the matrix equation AX B* + CY D* = E with arbitrary coefficient matrices A, B, C, D and the right-hand side E. This method determines the least squares solution (X, Y) with the least norm. It relies on the SVD and generalized SVD of the coefficient matrices and has complexity proportional to the cost of these SVDs.

KW - Least norm solution

KW - Matrix equation

KW - Singular value decomposition

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Least squares solution of matrix equation AX B* + CY D* = E*

Abstract

Keywords

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