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, $\sup_{W\in D}||(W^{\frac{1}{2}}A)^†W^{\frac{1}{2}}||_2=(\min_i \sigma_+(A^{(i)})^{-1}$, in which $(A^{(i)})$is a submatrix of A formed with $r = (\rm{rank}(A))$ 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 $W(\in D)$ are fixed with $W$ severely stiff. We show that in this case the weighted pseudoinverse $W^{\frac{1}{2}}A)^†W^{\frac{1}{2}}$ is close to a multi-level constrained weighted pseudoinverse therefore $||(W^{\frac{1}{2}}A)^†W^{\frac{1}{2}}||_2$ 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.