rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Structured Matrix Based Methods for Approximate Polynomial GCD
  name:
    name part: Boito, Paola
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: it
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    reformatting quality: access
    form: remote
    extent: 1 online resource (250 pages)
  abstract: 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.
  table of contents: 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.
  note: by Paola Boito.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Algebra
  subject:
    topic: Algebra
  subject:
    topic: Mathematics
  classification: QA150-272
  classification: 512
  related item:
    title info:
      title: Tesi/Theses ; 15
  identifier: 9788876423819
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record creation date: 120116
    record change date: 20210728125100.0
    record identifier: in00003518445