Year: 2004
Author: Musheng Wei
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 3 : pp. 427–436
Abstract
It is known that for a given matrix A of rank r, and a set D of positive diagonal matrices, supW∈D||(W12A)†W12||2=(miniσ+(A(i))−1, in which (A(i))is a submatrix of A formed with r=(rank(A)) rows of A, such that (A(i)) has full row rank r. In many practical applications this value is too large to be used.
In this paper we consider the case that both A and W(∈D) are fixed with W severely stiff. We show that in this case the weighted pseudoinverse W12A)†W12 is close to a multi-level constrained weighted pseudoinverse therefore ||(W12A)†W12||2 is uniformly bounded. We also prove that in this case the solution set the stiffly weighted least squares problem is close to that of corresponding multi-level constrained least squares problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JCM-10316
Journal of Computational Mathematics, Vol. 22 (2004), Iss. 3 : pp. 427–436
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Weighted least squares Stiff Multi-Level constrained pseudoinverse.