| 000 | 02570nam a22004335i 4500 | ||
|---|---|---|---|
| 001 | 978-88-7642-381-9 | ||
| 003 | DE-He213 | ||
| 005 | 20140220083822.0 | ||
| 007 | cr nn 008mamaa | ||
| 008 | 120116s2011 it | s |||| 0|eng d | ||
| 020 |
_a9788876423819 _9978-88-7642-381-9 |
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| 024 | 7 |
_a10.1007/978-88-7642-381-9 _2doi |
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| 050 | 4 | _aQA150-272 | |
| 072 | 7 |
_aPBF _2bicssc |
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| 072 | 7 |
_aMAT002000 _2bisacsh |
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| 082 | 0 | 4 |
_a512 _223 |
| 100 | 1 |
_aBoito, Paola. _eauthor. |
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| 245 | 1 | 0 |
_aStructured Matrix Based Methods for Approximate Polynomial GCD _h[electronic resource] / _cby Paola Boito. |
| 264 | 1 |
_aPisa : _bEdizioni della Normale, _c2011. |
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| 300 |
_a250p. _bonline resource. |
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| 336 |
_atext _btxt _2rdacontent |
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| 337 |
_acomputer _bc _2rdamedia |
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| 338 |
_aonline resource _bcr _2rdacarrier |
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| 347 |
_atext file _bPDF _2rda |
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| 490 | 1 |
_aTesi/Theses ; _v15 |
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| 505 | 0 | _ai. 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 | _aDefining 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 | _aMathematics. | |
| 650 | 0 | _aAlgebra. | |
| 650 | 1 | 4 | _aMathematics. |
| 650 | 2 | 4 | _aAlgebra. |
| 710 | 2 | _aSpringerLink (Online service) | |
| 773 | 0 | _tSpringer eBooks | |
| 776 | 0 | 8 |
_iPrinted edition: _z9788876423802 |
| 830 | 0 |
_aTesi/Theses ; _v15 |
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| 856 | 4 | 0 | _uhttp://dx.doi.org/10.1007/978-88-7642-381-9 |
| 912 | _aZDB-2-SMA | ||
| 999 |
_c108915 _d108915 |
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