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A minimum norm approach for low-rank approximations of a matrix

โœ Scribed by Achiya Dax

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
367 KB
Volume
234
Category
Article
ISSN
0377-0427

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โœฆ Synopsis

The problems of calculating a dominant eigenvector or a dominant pair of singular vectors, arise in several large scale matrix computations. In this paper we propose a minimum norm approach for solving these problems. Given a matrix, A, the new method computes a rankone matrix that is nearest to A, regarding the Frobenius matrix norm. This formulation paves the way for effective minimization techniques. The methods proposed in this paper illustrate the usefulness of this idea. The basic iteration is similar to that of the power method, but the rate of convergence is considerably faster. Numerical experiments are included.

๐Ÿ“œ SIMILAR VOLUMES

Existence of a low rank or โ„‹-matrix appr
Existence of a low rank or โ„‹-matrix approximant to the solution of a Sylvester equation
โœ L. Grasedyck ๐Ÿ“‚ Article ๐Ÿ“… 2004 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 190 KB

## Abstract We consider the Sylvester equation __AX__โˆ’__XB__+__C__=0 where the matrix __C__โˆˆโ„‚^__n__ร—__m__^ is of low rank and the spectra of __A__โˆˆโ„‚^__n__ร—__n__^ and __B__โˆˆโ„‚^__m__ร—__m__^ are separated by a line. We prove that the singular values of the solution X decay exponentially, that means for