| Publisher | Academy of Sciences of the Czech Republic | ||
|---|---|---|---|
| Format | 125.2KB PDF | Date added | 12 Jun 2008 |
| Topics | Bandwidth Issues, Software Engineering | ||
| Downloads | 2 | ||
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.
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