| Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA241.SPR FCT 82929 (Browse shelf) | 1 | Available |
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| QA241.SPR FCT 82153 Elementary number theory, cryptography and codes | QA241.SPR FCT 82294 Teoria dei numeri | QA241.SPR FCT 82462 Eta products and theta series identities | QA241.SPR FCT 82929 Structured matrix based methods for approximate polynomial GCD | QA241.SPR FCT 94279 Introduction to modern number theory | QA241.SPR FCT 94641 Number theory | QA241.SPR FCT 94813 Analytic number theory |
Colocação: Online
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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