A general condition number for polynomials (Q2840398)
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scientific article; zbMATH DE number 6189190
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A general condition number for polynomials |
scientific article; zbMATH DE number 6189190 |
Statements
18 July 2013
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polynomial condition number
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polynomial basis
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orthogonal polynomial
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Clenshaw algorithm
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floating-point arithmetic
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running-error bound
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Bernstein polynomials
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A general condition number for polynomials (English)
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The condition number of a polynomial with respect to a certain basis is an important quantity when it comes to the actual evaluation of this polynomial in finite precision arithmetic. The paper is devoted to the development of a general concept for such condition numbers that includes the well-known special cases where the basis consists of monomials or Bernstein polynomials and, in particular, allows to treat bases consisting of orthogonal polynomials. The properties of this condition number are studied in detail, and applications to some important special cases are discussed.
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