APPROXIMATION OF A SINGULAR MATRIX USING A D-INVERSE NONSINGULAR MATRIX

Authors
QANNARI A QANNARI EM
Citation
A. Qannari et Em. Qannari, APPROXIMATION OF A SINGULAR MATRIX USING A D-INVERSE NONSINGULAR MATRIX, RAIRO. Recherche operationnelle, 27(3), 1993, pp. 319-335
Citations number
8
Categorie Soggetti
Operatione Research & Management Science","Operatione Research & Management Science
Journal title
RAIRO. Recherche operationnelle → ACNP
ISSN journal
03990559
Volume
27
Issue
3
Year of publication
1993
Pages
319 - 335
Database
ISI
SICI code
0399-0559(1993)27:3<319:AOASMU>2.0.ZU;2-X
Abstract
We discuss an approximation (with respect to Hilbert-Schmidt norm) of a singular matrix by a non singular matrix with a given determinant. W e prove the existence and unicity of this matrix. We use this result t o define the D-inverse of a matrix by requiring the determinant to be the product of the nonzero singular values of the given matrix. We dis cuss the interest of this approach for improving the conditioning of a given matrix.