Generalized finite algorithms for constructing hermitian matrices with prescribed diagonal and spectrum

In this paper, we present new algorithms that can replace the diagonal entries of a Hermitian matrix by any set of diagonal entries that majorize the original set without altering the eigenvalues of the matrix. They perform this feat by applying a sequence of (N-1) or fewer plane rotations, where N...

Full description

Saved in:
Bibliographic Details
Published in:SIAM journal on matrix analysis and applications 2005-01, Vol.27 (1), p.61-71
Main Authors: DHILLON, Inderjit S, HEATH, Robert W, SUSTIK, Matyas A, TROPP, Joel A
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Eigenvalues
Exact sciences and technology
Linear and multilinear algebra, matrix theory
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Sciences and techniques of general use
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we present new algorithms that can replace the diagonal entries of a Hermitian matrix by any set of diagonal entries that majorize the original set without altering the eigenvalues of the matrix. They perform this feat by applying a sequence of (N-1) or fewer plane rotations, where N is the dimension of the matrix. Both the Bendel--Mickey and the Chan--Li algorithms are special cases of the proposed procedures. Using the fact that a positive semidefinite matrix can always be factored as $\mtx{X^\adj X}$, we also provide more efficient versions of the algorithms that can directly construct factors with specified singular values and column norms. We conclude with some open problems related to the construction of Hermitian matrices with joint diagonal and spectral properties.
ISSN:0895-4798
1095-7162
DOI:10.1137/S0895479803438183