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The Resource Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method, by Yuli Eidelman, Israel Gohberg, Iulian Haimovici, (electronic resource)

Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method, 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 second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods for computing eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms also being derived for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide a fast solver for the polynomial root finding problem. 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
XI, 359 pages
Contents
  • Part 5. The eigenvalue structure of order one quasiseparable matrices
  • 21. Quasiseparable of order one matrices. Characteristic polynomials
  • 22. Eigenvalues with geometric multiplicity one
  • 23. Kernels of quasiseparable of order one matrices
  • 24. Multiple eigenvalues
  • Part 6. Divide and conquer method for eigenproblems
  • 25. Divide step
  • 26. Conquer step and rational matrix functions eigenproblem
  • 27. Complete algorithm for Hermitian matrices
  • 28. Complete algorithm for unitary Hessenberg matrices
  • Part 7. Algorithms for qr iterations and for reduction to Hessenberg form
  • 29. The QR iteration method for eigenvalues
  • 30. The reduction to Hessenberg form
  • 31. The implicit QR iteration method for eigenvalues of upper Hessenberg matrices
  • Part 8. QR iterations for companion matrices
  • 32. Companion and unitary matrices
  • 33. Explicit methods
  • 34. Implicit methods with compression
  • 35. The factorization based implicit method
  • 36. Implicit algorithms based on the QR representation
  • Bibliography
Isbn
9783034806121
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0612-1
Instance
Label
Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method
Title
Separable Type Representations of Matrices and Fast Algorithms
Title remainder
Volume 2 Eigenvalue Method
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 second volume, consisting of four parts, addresses the eigenvalue problem for matrices with quasiseparable structure and applications to the polynomial root finding problem. In the first part the properties of the characteristic polynomials of principal leading submatrices, the structure of eigenspaces and the basic methods for computing eigenvalues are studied in detail for matrices with quasiseparable representation of the first order. The second part is devoted to the divide and conquer method, with the main algorithms also being derived for matrices with quasiseparable representation of order one. The QR iteration method for some classes of matrices with quasiseparable representations of any order is studied in the third part. This method is then used in the last part in order to provide a fast solver for the polynomial root finding problem. 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
235
http://library.link/vocab/subjectName
  • Mathematics
  • Matrices
  • Numerical analysis
Label
Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method, by Yuli Eidelman, Israel Gohberg, Iulian Haimovici, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0612-1
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 5. The eigenvalue structure of order one quasiseparable matrices -- 21. Quasiseparable of order one matrices. Characteristic polynomials -- 22. Eigenvalues with geometric multiplicity one -- 23. Kernels of quasiseparable of order one matrices -- 24. Multiple eigenvalues -- Part 6. Divide and conquer method for eigenproblems -- 25. Divide step -- 26. Conquer step and rational matrix functions eigenproblem -- 27. Complete algorithm for Hermitian matrices -- 28. Complete algorithm for unitary Hessenberg matrices -- Part 7. Algorithms for qr iterations and for reduction to Hessenberg form -- 29. The QR iteration method for eigenvalues -- 30. The reduction to Hessenberg form -- 31. The implicit QR iteration method for eigenvalues of upper Hessenberg matrices -- Part 8. QR iterations for companion matrices -- 32. Companion and unitary matrices -- 33. Explicit methods -- 34. Implicit methods with compression -- 35. The factorization based implicit method -- 36. Implicit algorithms based on the QR representation -- Bibliography
Control code
978-3-0348-0612-1
Dimensions
unknown
Extent
XI, 359 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
9783034806121
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0612-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1067191450
Label
Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method, by Yuli Eidelman, Israel Gohberg, Iulian Haimovici, (electronic resource)
Link
https://eui.idm.oclc.org/login?url=http://dx.doi.org/10.1007/978-3-0348-0612-1
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 5. The eigenvalue structure of order one quasiseparable matrices -- 21. Quasiseparable of order one matrices. Characteristic polynomials -- 22. Eigenvalues with geometric multiplicity one -- 23. Kernels of quasiseparable of order one matrices -- 24. Multiple eigenvalues -- Part 6. Divide and conquer method for eigenproblems -- 25. Divide step -- 26. Conquer step and rational matrix functions eigenproblem -- 27. Complete algorithm for Hermitian matrices -- 28. Complete algorithm for unitary Hessenberg matrices -- Part 7. Algorithms for qr iterations and for reduction to Hessenberg form -- 29. The QR iteration method for eigenvalues -- 30. The reduction to Hessenberg form -- 31. The implicit QR iteration method for eigenvalues of upper Hessenberg matrices -- Part 8. QR iterations for companion matrices -- 32. Companion and unitary matrices -- 33. Explicit methods -- 34. Implicit methods with compression -- 35. The factorization based implicit method -- 36. Implicit algorithms based on the QR representation -- Bibliography
Control code
978-3-0348-0612-1
Dimensions
unknown
Extent
XI, 359 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
9783034806121
Level of compression
uncompressed
Media category
computer
Media MARC source
rdamedia.
Media type code
  • c
Other control number
10.1007/978-3-0348-0612-1
Other physical details
online resource.
Quality assurance targets
absent
Reformatting quality
access
Specific material designation
remote
System control number
(OCoLC)1067191450

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