Separable Type Representations of Matrices and Fast Algorithms

Part I. Basics on Separable, Semi-separable and Quasiseparable Representations of Matrices

1. Matrices with Separable Representation and Low Complexity Algorithms
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

2. The Minimal Rank Completion Problem
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

3. Matrices in Diagonal Plus Semiseparable Form
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

4. Quasiseparable Representations: The Basics
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

5. Quasiseparable Generators
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

6. Rank Numbers of Pairs of Mutually Inverse Matrices, Asplund Theorems
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

7. Unitary Matrices with Quasiseparable Representations
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

Part II. Completion of Matrices with Specified Bands

8. Completion to Green Matrices
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

9. Completion to Matrices with Band Inverses and with Minimal Ranks
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

10. Completion of Special Types of Matrices
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

11. Completion of Mutually Inverse Matrices
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

12. Completion to Unitary Matrices
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

Part III. Quasiseparable Representations of Matrices, Descriptor Systems with Boundary Conditions and First Applications

13. Quasiseparable Representations and Descriptor Systems with Boundary Conditions
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

14. The First Inversion Algorithms
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

15. Inversion of Matrices in Diagonal Plus Semiseparable Form
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

16. Quasiseparable/Semiseparable Representations and One-direction Systems
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

17. Multiplication of Matrices
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

Part IV. Factorization and Inversion

18. The LDU Factorization and Inversion
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

19. Scalar Matrices with Quasiseparable Order One
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

20. The QR-Factorization Based Method
Yuli Eidelman, Israel Gohberg, Iulian Haimovici

Keywords: Mathematics, Linear and Multilinear Algebras, Matrix Theory, Numerical Analysis