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Published June 22, 2005 | public
Journal Article Open

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 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.

Additional Information

©2005 Society for Industrial and Applied Mathematics. Received by the editors November 21, 2003; accepted for publication (in revised form) by U. Helmke September 24, 2004; published electronically June 22, 2005. The research of this author [I.S.D.] was supported by NSF CAREER Award ACI-0093404.


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