A Chebyshev polynomial interval-searching method (``Lanczos economization'') for solving a nonlinear equation with application to the nonlinear eigenvalue problem (Q1891069)
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scientific article; zbMATH DE number 758610
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A Chebyshev polynomial interval-searching method (``Lanczos economization'') for solving a nonlinear equation with application to the nonlinear eigenvalue problem |
scientific article; zbMATH DE number 758610 |
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A Chebyshev polynomial interval-searching method (``Lanczos economization'') for solving a nonlinear equation with application to the nonlinear eigenvalue problem (English)
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24 October 1995
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Assume that we want to compute some zeros of a function \(f\) and that the evaluation of \(f(x)\) for a given value of \(x\) is expensive. In this case it may be better to first compute zeros of a polynomial approximation \(f_ N\) than to apply Newton's method directly. This is elucidated for the computation of eigenvalues via zeros of determinants. \{Reviewer's remark: The computation of eigenvalues via the characteristic polynomial can be recommended only in some well-known special cases.\}.
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Chebyshev polynomial interval-searching method
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Lanczos economization
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nonlinear eigenvalue problem
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approximation of zeros
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polynomial approximation
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Newton's method
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eigenvalues
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zeros of determinants
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