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

Eidelman, Yuli; Gohberg, Israel; Haimovici, Iulian

Brossura

ISBN 10: 3034806078 ISBN 13: 9783034806077

Casa editrice: Birkhäuser, 2013

Riassunto

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.​

Dettagli dell'edizione

• Editore: Birkhäuser
• Data di pubblicazione: 2013
• Lingua: Inglese
• ISBN 10: 3034806078
• ISBN 13: 9783034806077
• Rilegatura: Paperback
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile