Structured Matrix Based Methods for Approximate Polynomial GCD (Record no. 108915)
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| 000 -LEADER | |
|---|---|
| fixed length control field | 02570nam a22004335i 4500 |
| 001 - CONTROL NUMBER | |
| control field | 978-88-7642-381-9 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | DE-He213 |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20140220083822.0 |
| 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 | 120116s2011 it | s |||| 0|eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9788876423819 |
| -- | 978-88-7642-381-9 |
| 024 7# - OTHER STANDARD IDENTIFIER | |
| Standard number or code | 10.1007/978-88-7642-381-9 |
| Source of number or code | doi |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA150-272 |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | PBF |
| Source | bicssc |
| 072 #7 - SUBJECT CATEGORY CODE | |
| Subject category code | MAT002000 |
| Source | bisacsh |
| 082 04 - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512 |
| Edition number | 23 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Boito, Paola. |
| Relator term | author. |
| 245 10 - TITLE STATEMENT | |
| Title | Structured Matrix Based Methods for Approximate Polynomial GCD |
| Medium | [electronic resource] / |
| Statement of responsibility, etc | by Paola Boito. |
| 264 #1 - | |
| -- | Pisa : |
| -- | Edizioni della Normale, |
| -- | 2011. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 250p. |
| 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 | Tesi/Theses ; |
| Volume number/sequential designation | 15 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | i. Introduction -- ii. Notation -- 1. Approximate polynomial GCD -- 2. Structured and resultant matrices -- 3. The Euclidean algorithm -- 4. Matrix factorization and approximate GCDs -- 5. Optimization approach -- 6. New factorization-based methods -- 7. A fast GCD algorithm -- 8. Numerical tests -- 9. Generalizations and further work -- 10. Appendix A: Distances and norms -- 11. Appendix B: Special matrices -- 12. Bibliography -- 13. Index. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Defining and computing a greatest common divisor of two polynomials with inexact coefficients is a classical problem in symbolic-numeric computation. The first part of this book reviews the main results that have been proposed so far in the literature. As usual with polynomial computations, the polynomial GCD problem can be expressed in matrix form: the second part of the book focuses on this point of view and analyses the structure of the relevant matrices, such as Toeplitz, Toepliz-block and displacement structures. New algorithms for the computation of approximate polynomial GCD are presented, along with extensive numerical tests. The use of matrix structure allows, in particular, to lower the asymptotic computational cost from cubic to quadratic order with respect to polynomial degree. |
| 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 | Algebra. |
| 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 | Algebra. |
| 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 | 9788876423802 |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Tesi/Theses ; |
| Volume number/sequential designation | 15 |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | http://dx.doi.org/10.1007/978-88-7642-381-9 |
| 912 ## - | |
| -- | ZDB-2-SMA |
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