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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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Bibliographic Details
Main Authors: Eidelman, Yuli, Gohberg, Israel (Author), Haimovici, Iulian (Author)
Format: eBook
Language:English
Published: Basel Birkhäuser 2014, 2014
Edition:1st ed. 2014
Series:Operator Theory: Advances and Applications
Subjects:
Numerical Analysis
Linear Algebra
Algebras, Linear
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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

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