| 书目名称 | Structured Matrix Based Methods for Approximate Polynomial GCD |
| 编辑 | Paola Boito |
| 视频video | |
| 概述 | Topics situated at the crossroads between two fields of increasing interest to the mathematical community: symbolic-numeric polynomial computation and structured numerical linear algebra.Survey of the |
| 丛书名称 | Publications of the Scuola Normale Superiore |
| 图书封面 |  |
| 描述 | 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. |
| 出版日期 | Book 2011 |
| 关键词 | displacement structured matrices; polynomial computation; structured numerical linear algebra |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-88-7642-381-9 |
| isbn_softcover | 978-88-7642-380-2 |
| isbn_ebook | 978-88-7642-381-9Series ISSN 2239-1460 Series E-ISSN 2532-1668 |
| issn_series | 2239-1460 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
发表于 2025-3-21 18:32:26
