A relative backward perturbation theorem for the eigenvalue problem (Q1262696)
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scientific article; zbMATH DE number 4124889
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A relative backward perturbation theorem for the eigenvalue problem |
scientific article; zbMATH DE number 4124889 |
Statements
A relative backward perturbation theorem for the eigenvalue problem (English)
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1989
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If \(| \cdot |\) denotes absolute values taken componentwise the following statement is formulated: If \(| r| =| A\hat x-{\hat \lambda}\hat x| \leq \eta | A| | \hat x|\) holds for an approximate eigenpair (\({\hat \lambda}\),\^x) of A, then there exists a perturbation matrix E satisfying \(| E| \leq \eta | A|\) such that (\({\hat \lambda}\),\^x) is an exact eigenpair of the matrix \(A+E\).
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error bound
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eigenvalue problem
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backward analysis
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perturbation matrix
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eigenpair
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