Structured matrix based methods for approximate polynomial GCD
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 poly...
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| Format: | Livre numérique |
| Sprog: | Anglais |
| Udgivet: |
Pisa :
Scuola Normale Superiore
[20..].
Cham : Springer Nature |
| Udgivelse: | 1st ed. 2011. |
| Serier: | Theses (Scuola Normale Superiore)
15 |
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| Online adgang: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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L'impression du document génère xvi-199 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Structured Matrix Based Methods for Approximate Polynomial GCD, Texte imprimé, 9788876423802 |
| LEADER | 03281nam a22003857a 4500 | ||
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| 001 | 974345 | ||
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| 009 | PPN163561915 | ||
| 020 | |a 9788876423819 (en ligne) | ||
| 041 | 0 | |a eng | |
| 082 | |a 512 | ||
| 100 | 1 | |a Boito, Paola. | |
| 245 | 1 | 0 | |a Structured matrix based methods for approximate polynomial GCD |c Paola Boito. |
| 250 | |a 1st ed. 2011. | ||
| 260 | |a Pisa : |b Scuola Normale Superiore. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Theses (Scuola Normale Superiore) |v 15 |x 2532-1668 | |
| 500 | |a L'impression du document génère xvi-199 p. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 502 | |a tesi. Matematica. Scuela normale superiore Pisa. 2007 | ||
| 504 | |a Notes bibliogr. Index | ||
| 505 | 1 | |a 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. | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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. . | ||
| 650 | |a Polynômes | ||
| 650 | |a Théorie des diviseurs | ||
| 776 | 0 | |t Structured Matrix Based Methods for Approximate Polynomial GCD |b Texte imprimé |z 9788876423802 | |
| 856 | 4 | |q PDF |u https://doi.org/10.1007/978-88-7642-381-9 |z Accès sur la plateforme de l'éditeur | |
| 856 | 4 | |u https://revue-sommaire.istex.fr/ark:/67375/8Q1-LPF67MFH-P |z Accès sur la plateforme Istex | |
| 856 | 4 | |5 452349901:750609133 |u https://ezproxy.univ-orleans.fr/login?url=https://dx.doi.org/10.1007/978-88-7642-381-9 |z Accès Université d'Orléans | |
| 856 | 4 | |5 180339901:753968584 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-88-7642-381-9 |z Accès INSA CVL | |
| 997 | |0 974345 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||