### 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 | |

State | Published - 2003 |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*SIAM Journal on Matrix Analysis and Applications*, vol. 24, no. 3, pp. 802-808. https://doi.org/10.1137/S0895479802401059

}

TY - JOUR

T1 - Least squares solution of matrix equation AX B* + CY D* = E*

AU - Shim, Sang Yeun

AU - Chen, Yu

PY - 2003

Y1 - 2003

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=0042915997&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042915997&partnerID=8YFLogxK

U2 - 10.1137/S0895479802401059

DO - 10.1137/S0895479802401059

M3 - Article

AN - SCOPUS:0042915997

VL - 24

SP - 802

EP - 808

JO - SIAM Journal on Matrix Analysis and Applications

JF - SIAM Journal on Matrix Analysis and Applications

SN - 0895-4798

IS - 3

ER -