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: Separable Type Representations of Matrices and Fast Algorithms
    sub title: Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms
  name:
    name part: Eidelman, Yuli.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Gohberg, Israel.
    role:
      role term: author.
  name:
    name part: Haimovici, Iulian.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XV, 399 p. online resource.
  abstract: This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The primary focus is on fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work examines algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is mainly theoretical in character, introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part, where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part includes factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structures. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike.
  table of contents: Part 1. Basics on separable, semiseparable and quasiseparable representations of matrices -- 1. Matrices with separable representation and low complexity algorithms -- 2. The minimal rank completion problem -- 3. Matrices in diagonal plus semiseparable form -- 4. Quasiseparable representations: the basics -- 5. Quasiseparable generators -- 6. Rank numbers of pairs of mutually inverse matrices, Asplund theorems -- 7. Unitary matrices with quasiseparable representations -- Part 2. Completion of matrices with specified bands -- 8. Completion to Green matrices -- 9. Completion to matrices with band inverses and with minimal ranks -- 10. Completion of special types of matrices -- 11. Completion of mutually inverse matrices -- 12. Completion to unitary matrices -- Part 3. Quasiseparable representations of matrices, descriptor systems with boundary conditions and first applications -- 13. Quasiseparable representations and descriptor systems with boundary conditions -- 14. The first inversion algorithms -- 15. Inversion of matrices in diagonal plus semiseparable form -- 16. Quasiseparable/semiseparable representations and one-direction systems -- 17. Multiplication of matrices -- Part 4. Factorization and inversion -- 18. The LDU factorization and inversion -- 19. Scalar matrices with quasiseparable order one -- 20. The QR factorization based method.
  note: by Yuli Eidelman, Israel Gohberg, Iulian Haimovici.
  subject:
    topic: Mathematics
  subject:
    topic: Matrix theory
  subject:
    topic: Algebra
  subject:
    topic: Numerical analysis
  subject:
    topic: Mathematics
  subject:
    topic: Linear and Multilinear Algebras, Matrix Theory
  subject:
    topic: Numerical Analysis
  classification: QA184-205
  classification: 512.5
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Operator Theory: Advances and Applications, 234
  identifier: 9783034806060
  identifier: http://dx.doi.org/10.1007/978-3-0348-0606-0
  record info:
    record creation date: 131008
    record change date: 20151103125343.0
    record identifier: 978-3-0348-0606-0