Separable Type Representations of Matrices and Fast Algorithms Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms /

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 algo...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Eidelman, Yuli (Autor), Gohberg, Israel (Autor), Haimovici, Iulian (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Basel : Springer Basel : Imprint: Birkhäuser, 2014.
Edición:1st ed. 2014.
Colección:Operator Theory: Advances and Applications, 234
Temas:
Algebras, Linear.
Numerical analysis.
Linear Algebra.
Numerical Analysis.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

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