A QR algorithm with variable iteration multiplicity (Q1378996)
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scientific article; zbMATH DE number 1115928
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A QR algorithm with variable iteration multiplicity |
scientific article; zbMATH DE number 1115928 |
Statements
A QR algorithm with variable iteration multiplicity (English)
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2 September 1998
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Each step of an implicit multishift QR algorithm consists of first applying an \(m\times m\) orthogonal transformation, determined by the shifts, which causes a bulge of size \(m\) on the Hessenberg matrix, and then to eliminate that bulge with a sequence of orthogonal transformations. This process may suffer from forward instability and it is discussed how the multiplicity \(m\) should be chosen and the implementation done, to avoid ill effects of this forward instability.
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variable iteration multiplicity
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implicit multishift QR algorithm
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Hessenberg matrix
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orthogonal transformations
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forward instability
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