Showing papers by "Israel Gohberg published in 2014"
Book•
01 Jan 2014
TL;DR: In this paper, the minimal rank completion problem is formulated as a function of the rank number of a pair of mutually inverse matrices, and a low complexity algorithm is proposed to solve it.
Abstract: 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.
3 citations
01 Jan 2014
TL;DR: In this paper, the authors apply the idea used in Section §13.4 for a general case of matrices with quasiseparable representations with invertible diagonal entries.
Abstract: Here we consider inversion methods for some classes of matrices and representations. In the first section we apply the idea used in Section §13.4 for a general case of matrices with quasiseparable representations with invertible diagonal entries. In the second section we discuss an inversion method for matrices with lower quasiseparable and upper semisiseparable representations, under some restrictions on generators. This method is based on the representation of the matrix as a sum of an invertible lower triangular matrix and a matrix of a small rank. The same results are obtained in the subsequent Chapter 16 via the system approach.
2 citations