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)
Resource Information
The item Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method, 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 2 Eigenvalue Method, 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 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
- 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
- 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
- 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
- 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)
- 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)
- 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
Library Links
Embed
Settings
Select options that apply then copy and paste the RDF/HTML data fragment to include in your application
Embed this data in a secure (HTTPS) page:
Layout options:
Include data citation:
<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/4bNwVCZe9rk/" 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/4bNwVCZe9rk/">Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method, 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>
Note: Adjust the width and height settings defined in the RDF/HTML code fragment to best match your requirements
Preview
Cite Data - Experimental
Data Citation of the Item Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method, by Yuli Eidelman, Israel Gohberg, Iulian Haimovici, (electronic resource)
Copy and paste the following RDF/HTML data fragment to cite this resource
<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/4bNwVCZe9rk/" 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/4bNwVCZe9rk/">Separable Type Representations of Matrices and Fast Algorithms : Volume 2 Eigenvalue Method, 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>