White Papers
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.
- Publisher
- Academy of Sciences of the Czech Republic
- File Format
- Date Published
- Jul 11, 2008
- Format
- White Papers
- Topics
- Software Engineering, Bandwidth Issues
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