Separable Type Representations of Matrices and Fast Algorithms (Record no. 92442)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 04336nam a22004815i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-3-0348-0612-1 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20140220082506.0 |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr nn 008mamaa |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 131008s2014 sz | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9783034806121 |
| -- | 978-3-0348-0612-1 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-3-0348-0612-1 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA184-205 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBF |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT002050 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.5 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Eidelman, Yuli. |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Separable Type Representations of Matrices and Fast Algorithms |
| Medium | [electronic resource] : |
| Remainder of title | Volume 2 Eigenvalue Method / |
| Statement of responsibility, etc | by Yuli Eidelman, Israel Gohberg, Iulian Haimovici. |
| 264 #1 - | |
| -- | Basel : |
| -- | Springer Basel : |
| -- | Imprint: Birkhäuser, |
| -- | 2014. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | XI, 359 p. |
| Other physical details | online resource. |
| 336 ## - | |
| -- | text |
| -- | txt |
| -- | rdacontent |
| 337 ## - | |
| -- | computer |
| -- | c |
| -- | rdamedia |
| 338 ## - | |
| -- | online resource |
| -- | cr |
| -- | rdacarrier |
| 347 ## - | |
| -- | text file |
| -- | |
| -- | rda |
| 490 1# - SERIES STATEMENT | |
| Series statement | Operator Theory: Advances and Applications, |
| International Standard Serial Number | 0255-0156 ; |
| Volume number/sequential designation | 235 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 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. . |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | 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. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Matrix theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Numerical analysis. |
| 650 14 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Mathematics. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Linear and Multilinear Algebras, Matrix Theory. |
| 650 24 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name as entry element | Numerical Analysis. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Gohberg, Israel. |
| Relator term | author. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Haimovici, Iulian. |
| Relator term | author. |
| 710 2# - ADDED ENTRY--CORPORATE NAME | |
| Corporate name or jurisdiction name as entry element | SpringerLink (Online service) |
| 773 0# - HOST ITEM ENTRY | |
| Title | Springer eBooks |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Display text | Printed edition: |
| International Standard Book Number | 9783034806114 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Operator Theory: Advances and Applications, |
| -- | 0255-0156 ; |
| Volume number/sequential designation | 235 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-3-0348-0612-1 |
| 912 ## - | |
| -- | ZDB-2-SMA |
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