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On Orthogonal Reduction to Hessenberg Form With Small Bandwidth

Overview Numerous algorithms in numerical linear algebra are based on the reduction of a given matrix A to a more convenient form. One of the most useful types of such reduction is the orthogonal reduction to (upper) Hessenberg form. This reduction can be computed by the Arnoldi algorithm. When A is Hermitian, the resulting upper Hessenberg matrix is tridiagonal, which is a significant computational advantage. This paper studies necessary and sufficient conditions on A so that the orthogonal Hessenberg reduction yields a Hessenberg matrix with small bandwidth. This includes the orthogonal reduction to tridiagonal form as a special case. Orthogonality here is meant with respect to some given but unspecified inner product.

Further White Paper Details
Publisher	Academy of Sciences of the Czech Republic	File Format	PDF
Date Published	June 2008
Format	White Papers
Topics	Bandwidth Issues, Software Engineering

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