Perturbation analysis for the matrix least squares problem AXB = C

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:273

Article

Ling, Sitao¹  Wei, Musheng²  Jia, Zhigang³ 

[1] China Univ Min & Technol, Dept Math, State Key Lab Geomechan & Deep Underground Engn, Xuzhou 221116, Peoples R China

[2] Shanghai Univ, Shanghai Normal Univ, Coll Math & Sci, Sci Comp Key Lab, Shanghai 200234, Peoples R China

[3] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Peoples R China

关键词: Matrix equation;    Least squares solution;    Perturbation bound;    Norm-preserving dilation;   

DOI  :  10.1016/j.cam.2014.06.007

来源: Elsevier

【 摘 要 】

Let S and (S) over cap be two sets of solutions to matrix least squares problem (LSP) AXB = C and the perturbed matrix LSP (A) over cap(X) over cap(B) over cap = (C) over cap, respectively, where (A) over cap = A + Delta A, (B) over cap = B + Delta B, (C) over cap = C + Delta C, and Delta A, Delta B, Delta C are all small perturbation matrices. For any given X is an element of S, we deduce general formulas of the least squares solutions (X) over cap is an element of (S) over cap that are closest to X under appropriated norms, meanwhile, we present the corresponding distances between them. With the obtained results, we derive perturbation bounds for the nearest least squares solutions. At last, a numerical example is provided to verify our analysis. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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