Improved backward error bounds for LU and Cholesky factorizations (Q2923365)
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scientific article; zbMATH DE number 6356192
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Improved backward error bounds for LU and Cholesky factorizations |
scientific article; zbMATH DE number 6356192 |
Statements
15 October 2014
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LU factorization
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Cholesky factorization
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floating-point summation
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rounding error analysis
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triangular system solving
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backward error bound
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Improved backward error bounds for LU and Cholesky factorizations (English)
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New backward error bounds for LU and Cholesky factorizations are provided. To get these new bounds, the main ingradient is a refinement of the well-known Lemma 8.4 from \textit{N. J. Higham} [Accuracy and stability of numerical algorithms. 2nd ed. Philadelphia, PA: SIAM (2002; Zbl 1011.65010)] via some careful rounding error analysis of sums of one floating-point number and \(n-1\) real numbers.
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