The nearness problems for symmetric matrix with a submatrix constraint

✍ Scribed by Yongxin Yuan; Hua Dai

• Book ID: 104005442
• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 150 KB
• Volume: 213
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2007.01.033

✦ Synopsis

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): given a matrix X ∈ R n×p and symmetric matrices

) is the r × r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n×n symmetric matrix

where S E is the solution set of LSP. We show that the best approximation solution  is unique and derive an explicit formula for it.