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Journal of Mathematical Sciences

, Volume 168, Issue 3, pp 417–419 | Cite as

Root-squaring with DPR1 matrices

  • V. Y. Pan
Article
  • 23 Downloads

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.

Keywords

Recent Progress Characteristic Polynomial Fast Method Generalize Companion Classical Technique 
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References

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Copyright information

© Springer Science+Business Media, Inc. 2010

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceLehman College of the City University of New YorkBronxUSA

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