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Root-squaring with DPR1 matrices

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Recent progress in polynomial root-finding relies on employing the associated companion and generalized companion DPR1 matrices. (“DPR1” stands for “diagonal plus rank-one.”) We propose an algorithm that uses nearly linear arithmetic time to square a DPR1 matrix. Consequently, the algorithm squares the roots of the associated characteristic polynomial. This incorporates the classical techniques of polynomial root-finding by means of root-squaring into a new effective framework. Our approach is distinct from the earlier fast methods for squaring companion matrices. Bibliography: 13 titles.

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References

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Lehman College of the City University of New York, Bronx, USA

    V. Y. Pan

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  1. V. Y. Pan
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Correspondence to V. Y. Pan.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 373, 2009, pp. 189–193.

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Pan, V.Y. Root-squaring with DPR1 matrices. J Math Sci 168, 417–419 (2010). https://doi.org/10.1007/s10958-010-9993-y

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  • DOI: https://doi.org/10.1007/s10958-010-9993-y

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