Structured Matrix Based Methods for Approximate Polynomial GCD [recurso electrónico] / by Paola Boito.
Tipo de material: TextoSeries Tesi/Theses ; 15Editor: Pisa : Edizioni della Normale, 2011Descripción: 250p. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9788876423819Tema(s): Mathematics | Algebra | Mathematics | AlgebraFormatos físicos adicionales: Printed edition:: Sin títuloClasificación CDD: 512 Clasificación LoC:QA150-272Recursos en línea: Libro electrónicoTipo de ítem | Biblioteca actual | Colección | Signatura | Copia número | Estado | Fecha de vencimiento | Código de barras |
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Libro Electrónico | Biblioteca Electrónica | Colección de Libros Electrónicos | QA150 -272 (Browse shelf(Abre debajo)) | 1 | No para préstamo | 377429-2001 |
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QA150 -272 Discrete Mathematics in Statistical Physics | QA150 -272 Algebraic Geometry I | QA150 -272 Álgebra Linear | QA150 -272 Structured Matrix Based Methods for Approximate Polynomial GCD | QA150 -272 Algorithms for Quadratic Matrix and Vector Equations | QA164 -167.2 Geometric Etudes in Combinatorial Mathematics | QA164 -167.2 Notes on Introductory Combinatorics |
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.
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.
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