Articles liés à Applications of Number Theory to Numerical Analysis
Synopsis
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.
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Applications of Number Theory to Numerical Analysis
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Springer Berlin Heidelberg, 2011
ISBN 10 : 3642678319
ISBN 13 : 9783642678318
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Applications of Number Theory to Numerical Analysis
Edité par
Springer Berlin Heidelberg, 2011
ISBN 10 : 3642678319
ISBN 13 : 9783642678318
Neuf
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Taschenbuch. Etat : Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. N° de réf. du vendeur 9783642678318
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Applications of Number Theory to Numerical Analysis
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Springer Berlin Heidelberg Nov 2011, 2011
ISBN 10 : 3642678319
ISBN 13 : 9783642678318
Neuf
Taschenbuch
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 260 pp. Englisch. N° de réf. du vendeur 9783642678318
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Applications of Number Theory to Numerical Analysis
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Applications of Number Theory to Numerical Analysis
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Springer Berlin Heidelberg, Springer Berlin Heidelberg Nov 2011, 2011
ISBN 10 : 3642678319
ISBN 13 : 9783642678318
Neuf
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Taschenbuch. Etat : Neu. Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 260 pp. Englisch. N° de réf. du vendeur 9783642678318
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Applications of Number Theory to Numerical Analysis
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Applications of Number Theory to Numerical Analysis
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Applications of Number Theory to Numerical Analysis
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Applications of Number Theory to Numerical Analysis
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Applications of Number Theory to Numerical Analysis
Edité par
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ISBN 10 : 3642678319
ISBN 13 : 9783642678318
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