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A Highly Parallel Algorithm for Approximating All Zeros of a Polynomial with Only Real Zeros.

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Title: A Highly Parallel Algorithm for Approximating All Zeros of a Polynomial with Only Real Zeros.
Authors: Timlake, W. P., Patrick, Merrell L.1
Source: Communications of the ACM. Nov72, Vol. 15 Issue 11, p952-955. 4p.
Subjects: Algorithms, Polynomials, Newton-Raphson method, Stochastic convergence, Approximation theory, Mathematical functions
Abstract: An algorithm is described based on Newton's method I which simultaneously approximates all zeros of a polynomial with only real zeros. The algorithm, which is conceptually suitable for parallel computation, determines its own starting values so that convergence to the zeros is guaranteed. Multiple zeros and their multiplicity are readily determined. At no point in the method is polynomial deflation used. [ABSTRACT FROM AUTHOR]
Copyright of Communications of the ACM is the property of Association for Computing Machinery and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: <searchLink fieldCode="DE" term="%22Algorithms%22">Algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Newton-Raphson+method%22">Newton-Raphson method</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+convergence%22">Stochastic convergence</searchLink><br /><searchLink fieldCode="DE" term="%22Approximation+theory%22">Approximation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink>
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  Data: An algorithm is described based on Newton's method I which simultaneously approximates all zeros of a polynomial with only real zeros. The algorithm, which is conceptually suitable for parallel computation, determines its own starting values so that convergence to the zeros is guaranteed. Multiple zeros and their multiplicity are readily determined. At no point in the method is polynomial deflation used. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Communications of the ACM is the property of Association for Computing Machinery and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Text: English
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      – SubjectFull: Algorithms
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      – SubjectFull: Polynomials
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      – SubjectFull: Newton-Raphson method
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      – SubjectFull: Stochastic convergence
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      – SubjectFull: Approximation theory
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      – SubjectFull: Mathematical functions
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      – TitleFull: A Highly Parallel Algorithm for Approximating All Zeros of a Polynomial with Only Real Zeros.
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              Text: Nov72
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              Y: 1972
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