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Residual bounds on approximate solutions for the unitary eigenproblem
Umeå University, Faculty of Science and Technology, Departement of Computing Science.
1996 (English)In: Siam Journal on Matrix Analysis and Applications, Vol. 17, no 1, 69-82 p.Article in journal (Refereed) Published
Abstract [en]

Let A be an n x n unitary matrix, and let the columns of an n x l(l < n) matrix (X) over tilde(1) form an orthonormal basis for as approximate eigenspace <(chi)over tilde>(1) of A. Then there are two problems: How near is <(chi)over tilde>(1) to an eigenspace of A? How can we make use of the l x l matrix (X) over tilde(1)(H)A (X) over tilde(1) to get l approximate eigenvalues of A? This paper gives solutions to these problems. In particular, this paper reveals such a fact: One can use the eigenvalues of the unitary polar factor of (X) over tilde(1)(H)A (X) over tilde(1) (or the eigenvalues of the matrix (X) over tilde(1)(H)A (X) over tilde(1)) as 1 approximate eigenvalues of A, and the precision of the eigenvalues of the unitary polar factor of (X) over tilde(1)(H)A (X) over tilde(1) (or the eigenvalues of (X) over tilde(1)(H)A (X) over tilde(1)) as I approximate eigenvalues of A is higher than that of <(chi)over tilde>(1) as an approximate eigenspace of A.

Place, publisher, year, edition, pages
1996. Vol. 17, no 1, 69-82 p.
Identifiers
URN: urn:nbn:se:umu:diva-22000ISBN: 0895-4798 OAI: oai:DiVA.org:umu-22000DiVA: diva2:212263
Available from: 2009-04-21 Created: 2009-04-21 Last updated: 2009-04-21

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