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)
Resource Information
The item 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) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.This item is available to borrow from 1 library branch.
Resource Information
The item 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) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in European University Institute.
This item is available to borrow from 1 library branch.
- 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
- 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
- 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
- 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
- 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)
- 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)
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.eui.eu/portal/Separable-Type-Representations-of-Matrices-and/3HD23pRAoRU/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.eui.eu/portal/Separable-Type-Representations-of-Matrices-and/3HD23pRAoRU/">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)</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.eui.eu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.eui.eu/">European University Institute</a></span></span></span></span></div>
