Applications of Number Theory to Numerical Analysis:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1981
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Owing to the developments and applications of computer science, ma thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point. It'or example, from the seventeenth century till now, a great deal of effort was made in developing methods for approximating single integrals and there were only a few works on multiple quadrature until the 1950's. But in the past twenty years, a number of new methods have been devised of which the number theoretic method is an effective one. The number theoretic method may be described as follows. We use num ber theory to construct a sequence of uniformly distributed sets in the s dimensional unit cube G , where s ~ 2. Then we use the sequence to s reduce a difficult analytic problem to an arithmetic problem which may be calculated by computer. For example, we may use the arithmetic mean of the values of integrand in a given uniformly distributed set of G to ap s proximate the definite integral over G such that the principal order of the s error term is shown to be of the best possible kind, if the integrand satis fies certain conditions |
| Beschreibung: | 1 Online-Ressource (X, 244 p) |
| ISBN: | 9783642678295 9783642678318 |
| DOI: | 10.1007/978-3-642-67829-5 |
Internformat
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| 500 | |a Owing to the developments and applications of computer science, ma thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point. It'or example, from the seventeenth century till now, a great deal of effort was made in developing methods for approximating single integrals and there were only a few works on multiple quadrature until the 1950's. But in the past twenty years, a number of new methods have been devised of which the number theoretic method is an effective one. The number theoretic method may be described as follows. We use num ber theory to construct a sequence of uniformly distributed sets in the s dimensional unit cube G , where s ~ 2. Then we use the sequence to s reduce a difficult analytic problem to an arithmetic problem which may be calculated by computer. For example, we may use the arithmetic mean of the values of integrand in a given uniformly distributed set of G to ap s proximate the definite integral over G such that the principal order of the s error term is shown to be of the best possible kind, if the integrand satis fies certain conditions | ||
| 650 | 4 | |a Mathematics | |
| 650 | 4 | |a Numerical analysis | |
| 650 | 4 | |a Number theory | |
| 650 | 4 | |a Number Theory | |
| 650 | 4 | |a Numerical Analysis | |
| 650 | 4 | |a Mathematik | |
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Datensatz im Suchindex
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| author | Keng, Hua Loo |
| author_facet | Keng, Hua Loo |
| author_role | aut |
| author_sort | Keng, Hua Loo |
| author_variant | h l k hl hlk |
| building | Verbundindex |
| bvnumber | BV042422923 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863786600 (DE-599)BVBBV042422923 |
| dewey-full | 512.7 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.7 |
| dewey-search | 512.7 |
| dewey-sort | 3512.7 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-67829-5 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T01:21:12Z |
| institution | BVB |
| isbn | 9783642678295 9783642678318 |
| language | English |
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| publishDate | 1981 |
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| publisher | Springer Berlin Heidelberg |
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| spelling | Keng, Hua Loo Verfasser aut Applications of Number Theory to Numerical Analysis by Hua Loo Keng, Wang Yuan Berlin, Heidelberg Springer Berlin Heidelberg 1981 1 Online-Ressource (X, 244 p) txt rdacontent c rdamedia cr rdacarrier Owing to the developments and applications of computer science, ma thematicians began to take a serious interest in the applications of number theory to numerical analysis about twenty years ago. The progress achieved has been both important practically as well as satisfactory from the theoretical view point. It'or example, from the seventeenth century till now, a great deal of effort was made in developing methods for approximating single integrals and there were only a few works on multiple quadrature until the 1950's. But in the past twenty years, a number of new methods have been devised of which the number theoretic method is an effective one. The number theoretic method may be described as follows. We use num ber theory to construct a sequence of uniformly distributed sets in the s dimensional unit cube G , where s ~ 2. Then we use the sequence to s reduce a difficult analytic problem to an arithmetic problem which may be calculated by computer. For example, we may use the arithmetic mean of the values of integrand in a given uniformly distributed set of G to ap s proximate the definite integral over G such that the principal order of the s error term is shown to be of the best possible kind, if the integrand satis fies certain conditions Mathematics Numerical analysis Number theory Number Theory Numerical Analysis Mathematik Zahlentheorie (DE-588)4067277-3 gnd rswk-swf Analysis (DE-588)4001865-9 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Numerische Mathematik (DE-588)4042805-9 gnd rswk-swf Zahlentheorie (DE-588)4067277-3 s Analysis (DE-588)4001865-9 s Numerisches Verfahren (DE-588)4128130-5 s 1\p DE-604 Numerische Mathematik (DE-588)4042805-9 s 2\p DE-604 Yuan, Wang Sonstige oth https://doi.org/10.1007/978-3-642-67829-5 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 | Keng, Hua Loo Applications of Number Theory to Numerical Analysis Mathematics Numerical analysis Number theory Number Theory Numerical Analysis Mathematik Zahlentheorie (DE-588)4067277-3 gnd Analysis (DE-588)4001865-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| subject_GND | (DE-588)4067277-3 (DE-588)4001865-9 (DE-588)4128130-5 (DE-588)4042805-9 |
| title | Applications of Number Theory to Numerical Analysis |
| title_auth | Applications of Number Theory to Numerical Analysis |
| title_exact_search | Applications of Number Theory to Numerical Analysis |
| title_full | Applications of Number Theory to Numerical Analysis by Hua Loo Keng, Wang Yuan |
| title_fullStr | Applications of Number Theory to Numerical Analysis by Hua Loo Keng, Wang Yuan |
| title_full_unstemmed | Applications of Number Theory to Numerical Analysis by Hua Loo Keng, Wang Yuan |
| title_short | Applications of Number Theory to Numerical Analysis |
| title_sort | applications of number theory to numerical analysis |
| topic | Mathematics Numerical analysis Number theory Number Theory Numerical Analysis Mathematik Zahlentheorie (DE-588)4067277-3 gnd Analysis (DE-588)4001865-9 gnd Numerisches Verfahren (DE-588)4128130-5 gnd Numerische Mathematik (DE-588)4042805-9 gnd |
| topic_facet | Mathematics Numerical analysis Number theory Number Theory Numerical Analysis Mathematik Zahlentheorie Analysis Numerisches Verfahren Numerische Mathematik |
| url | https://doi.org/10.1007/978-3-642-67829-5 |
| work_keys_str_mv | AT kenghualoo applicationsofnumbertheorytonumericalanalysis AT yuanwang applicationsofnumbertheorytonumericalanalysis |