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The Resource Separable Type Representations of Matrices and Fast Algorithms : Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms, by Yuli Eidelman, Israel Gohberg, Iulian Haimovici, (electronic resource)

Separable Type Representations of Matrices and Fast Algorithms : Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms, by Yuli Eidelman, Israel Gohberg, Iulian Haimovici, (electronic resource)

Creator
Author
Contributor
Summary
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
Language
eng
Work
Publication
Extent
XV, 399 pages
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
Isbn
9783034806060
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0606-0
Instance
Label
Separable Type Representations of Matrices and Fast Algorithms : Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms
Title
Separable Type Representations of Matrices and Fast Algorithms
Title remainder
Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms
Statement of responsibility
by Yuli Eidelman, Israel Gohberg, Iulian Haimovici
Creator
Contributor
Author
Subject
Language
eng
Summary
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
Member of
Cataloging source
IT-FiEUI
http://library.link/vocab/creatorDate
1955-
http://library.link/vocab/creatorName
Eidelman, Yuli
Image bit depth
0
Literary form
non fiction
http://library.link/vocab/relatedWorkOrContributorDate
1928-2009.
http://library.link/vocab/relatedWorkOrContributorName
  • Gohberg, I.
  • Haimovici, Iulian.
  • SpringerLink (Online service)
Series statement
  • Operator Theory: Advances and Applications,
  • Springer eBooks
Series volume
234
http://library.link/vocab/subjectName
  • Mathematics
  • Matrices
  • Numerical analysis
Label
Separable Type Representations of Matrices and Fast Algorithms : Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms, by Yuli Eidelman, Israel Gohberg, Iulian Haimovici, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0606-0
Instantiates
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
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
Control code
978-3-0348-0606-0
Dimensions
unknown
Extent
XV, 399 pages
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034806060
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0606-0
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)896283831
Label
Separable Type Representations of Matrices and Fast Algorithms : Volume 1 Basics. Completion Problems. Multiplication and Inversion Algorithms, by Yuli Eidelman, Israel Gohberg, Iulian Haimovici, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0606-0
Publication
Antecedent source
mixed
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier.
Color
not applicable
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent.
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
Control code
978-3-0348-0606-0
Dimensions
unknown
Extent
XV, 399 pages
File format
multiple file formats
Form of item
electronic
Governing access note
Use of this electronic resource may be governed by a license agreement which restricts use to the European University Institute community. Each user is responsible for limiting use to individual, non-commercial purposes, without systematically downloading, distributing, or retaining substantial portions of information, provided that all copyright and other proprietary notices contained on the materials are retained. The use of software, including scripts, agents, or robots, is generally prohibited and may result in the loss of access to these resources for the entire European University Institute community
Isbn
9783034806060
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0606-0
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)896283831

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