Discrete Iterations: A Metric Study
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1986
|
| Schriftenreihe: | Springer Series in Computational Mathematics
6 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | a c 9 h In presenting this monograph, I would like to indicate both its orientation as well as my personal reasons for being interested in discrete iterations (that is, iterations on a generally very large,jinite set). While working in numerical analysis I have been interested in two main aspects: - the algorithmic aspect: an iterative algorithm is a mathematical entity which behaves in a dynamic fashion. Even if it is started far from a solution, it will often tend to get closer and closer. - the mathematical aspect: this consists of a coherent and rigorous analy sis of convergence, with the aid of mathematical tools (these tools are mainly the use of norms for convergence proofs, the use of matrix algebra and so on). One may for example refer to the algorithmic and mathematical aspects of Newton's method in JRn as well as to the QR algorithm for eigenvalues of matrices. These two algorithms seem to me to be the most fascinating algorithms in numerical analysis, since both show a remarkable practical efficiency even though there exist relatively few global convergence results for them |
| Beschreibung: | 1 Online-Ressource (XVI, 198 p) |
| ISBN: | 9783642616075 9783642648823 |
| ISSN: | 0179-3632 |
| DOI: | 10.1007/978-3-642-61607-5 |
Internformat
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| 500 | |a a c 9 h In presenting this monograph, I would like to indicate both its orientation as well as my personal reasons for being interested in discrete iterations (that is, iterations on a generally very large,jinite set). While working in numerical analysis I have been interested in two main aspects: - the algorithmic aspect: an iterative algorithm is a mathematical entity which behaves in a dynamic fashion. Even if it is started far from a solution, it will often tend to get closer and closer. - the mathematical aspect: this consists of a coherent and rigorous analy sis of convergence, with the aid of mathematical tools (these tools are mainly the use of norms for convergence proofs, the use of matrix algebra and so on). One may for example refer to the algorithmic and mathematical aspects of Newton's method in JRn as well as to the QR algorithm for eigenvalues of matrices. These two algorithms seem to me to be the most fascinating algorithms in numerical analysis, since both show a remarkable practical efficiency even though there exist relatively few global convergence results for them | ||
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Datensatz im Suchindex
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| author | Robert, François |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 518 - Numerical analysis |
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| dewey-sort | 3518 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-61607-5 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
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| institution | BVB |
| isbn | 9783642616075 9783642648823 |
| issn | 0179-3632 |
| language | English |
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| spelling | Robert, François Verfasser aut Discrete Iterations A Metric Study by François Robert Berlin, Heidelberg Springer Berlin Heidelberg 1986 1 Online-Ressource (XVI, 198 p) txt rdacontent c rdamedia cr rdacarrier Springer Series in Computational Mathematics 6 0179-3632 a c 9 h In presenting this monograph, I would like to indicate both its orientation as well as my personal reasons for being interested in discrete iterations (that is, iterations on a generally very large,jinite set). While working in numerical analysis I have been interested in two main aspects: - the algorithmic aspect: an iterative algorithm is a mathematical entity which behaves in a dynamic fashion. Even if it is started far from a solution, it will often tend to get closer and closer. - the mathematical aspect: this consists of a coherent and rigorous analy sis of convergence, with the aid of mathematical tools (these tools are mainly the use of norms for convergence proofs, the use of matrix algebra and so on). One may for example refer to the algorithmic and mathematical aspects of Newton's method in JRn as well as to the QR algorithm for eigenvalues of matrices. These two algorithms seem to me to be the most fascinating algorithms in numerical analysis, since both show a remarkable practical efficiency even though there exist relatively few global convergence results for them Mathematics Numerical analysis Numerical Analysis Mathematik Diskrete Iteration (DE-588)4123072-3 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Iteration (DE-588)4123457-1 gnd rswk-swf Iteration (DE-588)4123457-1 s Numerische Mathematik (DE-588)4042805-9 s 1\p DE-604 Diskrete Iteration (DE-588)4123072-3 s 2\p DE-604 https://doi.org/10.1007/978-3-642-61607-5 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Robert, François Discrete Iterations A Metric Study Mathematics Numerical analysis Numerical Analysis Mathematik Diskrete Iteration (DE-588)4123072-3 gnd Numerische Mathematik (DE-588)4042805-9 gnd Iteration (DE-588)4123457-1 gnd |
| subject_GND | (DE-588)4123072-3 (DE-588)4042805-9 (DE-588)4123457-1 |
| title | Discrete Iterations A Metric Study |
| title_auth | Discrete Iterations A Metric Study |
| title_exact_search | Discrete Iterations A Metric Study |
| title_full | Discrete Iterations A Metric Study by François Robert |
| title_fullStr | Discrete Iterations A Metric Study by François Robert |
| title_full_unstemmed | Discrete Iterations A Metric Study by François Robert |
| title_short | Discrete Iterations |
| title_sort | discrete iterations a metric study |
| title_sub | A Metric Study |
| topic | Mathematics Numerical analysis Numerical Analysis Mathematik Diskrete Iteration (DE-588)4123072-3 gnd Numerische Mathematik (DE-588)4042805-9 gnd Iteration (DE-588)4123457-1 gnd |
| topic_facet | Mathematics Numerical analysis Numerical Analysis Mathematik Diskrete Iteration Numerische Mathematik Iteration |
| url | https://doi.org/10.1007/978-3-642-61607-5 |
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