The triangular matrices of Gaussian elimination and related decompositions (Q2785704)
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scientific article; zbMATH DE number 981867
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The triangular matrices of Gaussian elimination and related decompositions |
scientific article; zbMATH DE number 981867 |
Statements
The triangular matrices of Gaussian elimination and related decompositions (English)
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9 October 1997
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ill-conditioning
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linear systems
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triangular matrices
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Gaussian elimination
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QR-decomposition
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LU-decomposition
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lower bound
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smallest singular value
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0.8996715
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0.8793856
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0.8778782
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By deriving a new lower bound for the smallest singular value the author explains the observation that triangular systems obtained by \(LU\) or \(QR\) decomposition are frequently solved more accurately than their condition would warrant. He shows that this fact is closely connected to the rank-revealing character of these decompositions.
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