Calculating polynomial zeros on a local memory parallel computer |
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Authors: | TL Freeman |
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Affiliation: | Department of Mathematics, University of Manchester, Manchester, UK M13 9PL |
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Abstract: | We consider the calculation, on a local memory parallel computer, of all the zeros of an n th degree polynomial Pn(x) which has real coefficients. We describe a generic parallel algorith, which approximates all the zeros simultaneously and we give three specific examples of this algorithm which have orders of convergence two, three and four. We report extensive numerical tests of the algorithms; the fourth order algorithm is not robust, with many failures to convergence, whereas the other two algorithms are reliable and display very respectable parallel speedups for higher degree polynomials. |
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Keywords: | Parallel algorithms local memory parallel computers transputers polynomial zeros simultaneous polynomial root-finders |
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