Numerical algorithms based on analytic function values at roots of unity (Q2927834)
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scientific article; zbMATH DE number 6365781
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Numerical algorithms based on analytic function values at roots of unity |
scientific article; zbMATH DE number 6365781 |
Statements
4 November 2014
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polynomial interpolation
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barycentric formula
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Cauchy integral formula
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trapezoidal rule
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rational approximation
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eigenvalues
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roots of unity
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FEAST
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RATDISK
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Numerical algorithms based on analytic function values at roots of unity (English)
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The authors solve the following problem: given a function \(f(z)\) holomorphic or meromorphic in the closed unit disk and sampled at the \(n\)th roots of unity. By the help of polynomial and rational interpolation there are presented the methods for evaluation of approximation of the values \(f(z)\) or \(f^{(m)}(z)\) where \(z\) is a point in the disk. The presented method is used to the problem of computing of the eigenvalues in the unit disk of a matrix of large dimension. There is also presented the comparison of rational and polynomial approximation in the studied topic
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