Description: Separable Type Representations of Matrices and Fast Algorithms by Yuli Eidelman, Israel Gohberg, Iulian Haimovici The first applications of the quasiseparable and semiseparable structure are included in the third part where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. FORMAT Hardcover LANGUAGE English CONDITION Brand New Publisher Description This two-volume work presents a systematic theoretical and computational study of several types of generalizations of separable matrices. The main attention is paid to fast algorithms (many of linear complexity) for matrices in semiseparable, quasiseparable, band and companion form. The work is focused on algorithms of multiplication, inversion and description of eigenstructure and includes a large number of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is of a mainly theoretical character introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part contains factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structure. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and the accessible style the text will be useful to engineers, scientists, numerical analysts, computer scientists and mathematicians alike. Back Cover 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 algorithms of multiplication, inversion and description of eigenstructure and includes a wealth of illustrative examples throughout the different chapters. The first volume consists of four parts. The first part is mainly theoretical in character, introducing and studying the quasiseparable and semiseparable representations of matrices and minimal rank completion problems. Three further completions are treated in the second part. The first applications of the quasiseparable and semiseparable structure are included in the third part, where the interplay between the quasiseparable structure and discrete time varying linear systems with boundary conditions play an essential role. The fourth part includes factorization and inversion fast algorithms for matrices via quasiseparable and semiseparable structures. The work is based mostly on results obtained by the authors and their coauthors. Due to its many significant applications and accessible style, the text will be a valuable resource for engineers, scientists, numerical analysts, computer scientists and mathematicians alike. 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. Feature Self-contained monograph with material developed over the last 30 years Systematic theoretical and computational study of several types of generalizations of separable matrices Many illustrative examples in different chapters of the book Details ISBN3034806051 Author Iulian Haimovici Short Title SEPARABLE TYPE REPRESENTATIONS Series Operator Theory: Advances and Applications Language English ISBN-10 3034806051 ISBN-13 9783034806053 Media Book Format Hardcover Series Number 234 Birth 1955 Year 2013 Country of Publication Switzerland DEWEY 512.9434 Pages 399 Edition 2014th Subtitle Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms Illustrations XV, 399 p. DOI 10.1007/978-3-0348-0606-0 Publication Date 2013-10-22 Place of Publication Basel Imprint Birkhauser Verlag AG Publisher Birkhauser Verlag AG Edition Description 2014 ed. Audience Professional & Vocational We've got this At The Nile, if you're looking for it, we've got it. 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ISBN-13: 9783034806053
Book Title: Separable Type Representations of Matrices and Fast Algorithms
Number of Pages: 399 Pages
Language: English
Publication Name: Separable Type Representations of Matrices and Fast Algorithms: Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms
Publisher: Birkhauser Verlag Ag
Publication Year: 2013
Subject: Mathematics
Item Height: 235 mm
Item Weight: 787 g
Type: Textbook
Author: Yuli Eidelman, Israel Gohberg, Iulian Haimovici
Item Width: 155 mm
Format: Hardcover
