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

Sang Yeun Shim, Yu Chen

Research output: Contribution to journalArticle

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) 802-808 7 SIAM Journal on Matrix Analysis and Applications 24 3 https://doi.org/10.1137/S0895479802401059 Published - 2003

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Least-squares Solution
Singular value decomposition
Matrix Equation
Coefficient
Efficient Algorithms
Directly proportional
Norm
Costs
Arbitrary

Keywords

• Least norm solution
• Matrix equation
• Singular value decomposition

ASJC Scopus subject areas

• Algebra and Number Theory
• Analysis
• Applied Mathematics

Cite this

Least squares solution of matrix equation AX B* + CY D* = E*. / Shim, Sang Yeun; Chen, Yu.

In: SIAM Journal on Matrix Analysis and Applications, Vol. 24, No. 3, 2003, p. 802-808.

Research output: Contribution to journalArticle

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