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A numerical accuracy consideration in polynomial deflation

Authors: C. J. O'Neill and T. Downs
Journal: Math. Comp. 32 (1978), 1144-1146
MSC: Primary 65H05; Secondary 65G05
MathSciNet review: 502003
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Abstract: In a recent paper, Peters and Wilkinson described a composite deflation method which provides an accurate technique for the determination of the roots of a polynomial where these roots are widely spaced. By examples involving deflation by linear factors they demonstrated that the method was much more accurate than forward or backward deflation. In addition, they stated that the method could also be used when deflating by a quadratic factor or a polynomial of higher degree. In this short note it is shown that composite deflation by quadratic factors can lead to severe rounding error where two successive deflations by linear factors produce a perfectly accurate result.

References [Enhancements On Off] (What's this?)

  • [1] G. Peters and J. H. Wilkinson, Practical problems arising in the solution of polynomial equations, J. Inst. Math. Appl. 8 (1971), 16–35. MR 0298931
  • [2] T. Downs, On the inversion of a matrix of rational functions, Linear Algebra and Appl. 4 (1971), 1–10. MR 0281328
  • [3] Z. Bohte and J. Grad, On composite polynomial deflation by a quadratic factor, Glasnik Mat. Ser. III 12(32) (1977), no. 1, 199–208 (English, with Slovenian summary). MR 0461883

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Article copyright: © Copyright 1978 American Mathematical Society

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