Are the coefficients of a polynomial well-conditioned functions of its roots? (Q1203402)
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scientific article; zbMATH DE number 118294
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Are the coefficients of a polynomial well-conditioned functions of its roots? |
scientific article; zbMATH DE number 118294 |
Statements
Are the coefficients of a polynomial well-conditioned functions of its roots? (English)
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8 February 1993
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The author shows that the coefficients of a polynomial can be rather ill- conditioned functions of its given roots. In certain cases, the coefficients are well-conditioned. He introduces and studies the condition number for the sensitivity of the polynomial coefficients \(a_ k\) to changes in the root \(x_ 1\) and develops an algorithm to compute the condition numbers and to decide whether a given set of roots will generate the polynomial coefficients in an ill-conditioned way.
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ill-conditioned functions of its roots
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condition number
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polynomial coefficients
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