Structured Matrix Based Methods for Approximate Polynomial GCD

(Autor)

Buch | Softcover
250 Seiten
2011 | 2011 ed.
Scuola Normale Superiore (Verlag)
978-88-7642-380-2 (ISBN)

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Structured Matrix Based Methods for Approximate Polynomial GCD - Paola Boito
19,26 inkl. MwSt
Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree.

i. Introduction.- ii. Notation.- 1. Approximate polynomial GCD.- 2. Structured and resultant matrices.- 3. The Euclidean algorithm.- 4. Matrix factorization and approximate GCDs.- 5. Optimization approach.- 6. New factorization-based methods.- 7. A fast GCD algorithm.- 8. Numerical tests.- 9. Generalizations and further work.- 10. Appendix A: Distances and norms.- 11. Appendix B: Special matrices.- 12.Bibliography.- 13. Index.

Reihe/Serie Publications of the Scuola Normale Superiore ; 15
Theses (Scuola Normale Superiore)
Zusatzinfo 250 p.
Verlagsort Pisa
Sprache englisch
Maße 168 x 240 mm
Themenwelt Mathematik / Informatik Mathematik Algebra
Schlagworte displacement structured matrices • polynomial computation • structured numerical linear algebra
ISBN-10 88-7642-380-X / 887642380X
ISBN-13 978-88-7642-380-2 / 9788876423802
Zustand Neuware
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