Applications Of Number Theory To Numerical Analysis
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Applications Of Number Theory To Numerical Analysis
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Author : L.-K. Hua
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applications Of Number Theory To Numerical Analysis written by L.-K. Hua and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
From Great Discoveries In Number Theory To Applications
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Author : Michal Křížek
language : en
Publisher: Springer Nature
Release Date : 2021-09-21
From Great Discoveries In Number Theory To Applications written by Michal Křížek and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-21 with Mathematics categories.
This book provides an overview of many interesting properties of natural numbers, demonstrating their applications in areas such as cryptography, geometry, astronomy, mechanics, computer science, and recreational mathematics. In particular, it presents the main ideas of error-detecting and error-correcting codes, digital signatures, hashing functions, generators of pseudorandom numbers, and the RSA method based on large prime numbers. A diverse array of topics is covered, from the properties and applications of prime numbers, some surprising connections between number theory and graph theory, pseudoprimes, Fibonacci and Lucas numbers, and the construction of Magic and Latin squares, to the mathematics behind Prague’s astronomical clock. Introducing a general mathematical audience to some of the basic ideas and algebraic methods connected with various types of natural numbers, the book will provide invaluable reading for amateurs and professionals alike.
Number Theoretic Methods In Statistics
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Author : Kai-Tai Fang
language : en
Publisher: CRC Press
Release Date : 1993-12-01
Number Theoretic Methods In Statistics written by Kai-Tai Fang and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-01 with Mathematics categories.
This book is a survey of recent work on the application of number theory in statistics. The essence of number-theoretic methods is to find a set of points that are universally scattered over an s-dimensional unit cube. In certain circumstances this set can be used instead of random numbers in the Monte Carlo method. The idea can also be applied to other problems such as in experimental design. This book will illustrate the idea of number-theoretic methods and their application in statistics. The emphasis is on applying the methods to practical problems so only part-proofs of theorems are given.
Applications Of Number Theory To Numerical Analysis
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Author : S. K. Zaremba
language : en
Publisher: New York : Academic Press
Release Date : 1972
Applications Of Number Theory To Numerical Analysis written by S. K. Zaremba and has been published by New York : Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972 with Mathematics categories.
Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.
Elementary Theory And Application Of Numerical Analysis
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Author : David G. Moursund
language : en
Publisher: Courier Dover Publications
Release Date : 2013-04-22
Elementary Theory And Application Of Numerical Analysis written by David G. Moursund and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-22 with Mathematics categories.
This updated introduction to modern numerical analysis is a complete revision of a classic text originally written in Fortran but now featuring the programming language C++. It focuses on a relatively small number of basic concepts and techniques. Many exercises appear throughout the text, most with solutions. An extensive tutorial explains how to solve problems with C++.
Theory And Applications Of Numerical Analysis
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Author : G. M. Phillips
language : en
Publisher: Elsevier
Release Date : 1996-07-05
Theory And Applications Of Numerical Analysis written by G. M. Phillips and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-07-05 with Mathematics categories.
Theory and Applications of Numerical Analysis is a self-contained Second Edition, providing an introductory account of the main topics in numerical analysis. The book emphasizes both the theorems which show the underlying rigorous mathematics andthe algorithms which define precisely how to program the numerical methods. Both theoretical and practical examples are included. - a unique blend of theory and applications - two brand new chapters on eigenvalues and splines - inclusion of formal algorithms - numerous fully worked examples - a large number of problems, many with solutions
Numerical Analysis
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Author : Brian Sutton
language : en
Publisher: SIAM
Release Date : 2019-04-18
Numerical Analysis written by Brian Sutton and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-18 with Mathematics categories.
This textbook develops the fundamental skills of numerical analysis: designing numerical methods, implementing them in computer code, and analyzing their accuracy and efficiency. A number of mathematical problems?interpolation, integration, linear systems, zero finding, and differential equations?are considered, and some of the most important methods for their solution are demonstrated and analyzed. Notable features of this book include the development of Chebyshev methods alongside more classical ones; a dual emphasis on theory and experimentation; the use of linear algebra to solve problems from analysis, which enables students to gain a greater appreciation for both subjects; and many examples and exercises. Numerical Analysis: Theory and Experiments is designed to be the primary text for a junior- or senior-level undergraduate course in numerical analysis for mathematics majors. Scientists and engineers interested in numerical methods, particularly those seeking an accessible introduction to Chebyshev methods, will also be interested in this book.
Applications Of Number Theory To Numerical Analysis
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Author : S. K. Zaremba
language : en
Publisher: Academic Press
Release Date : 2014-05-10
Applications Of Number Theory To Numerical Analysis written by S. K. Zaremba and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
Applications of Number Theory to Numerical Analysis contains the proceedings of the Symposium on Applications of Number Theory to Numerical Analysis, held in Quebec, Canada, on September 9-14, 1971, under the sponsorship of the University of Montreal's Center for Research in Mathematics. The symposium provided a forum for discussing number theory and its applications to numerical analysis, tackling topics ranging from methods used in estimating discrepancy to the structure of linear congruential sequences. Comprised of 17 chapters, this book begins by considering some combinatorial problems studied experimentally on computing machines. The discussion then turns to experiments on optimal coefficients; a distribution problem in finite sets; and the statistical interdependence of pseudo-random numbers generated by the linear congruential method. Subsequent chapters deal with lattice structure and reduced bases of random vectors generated by linear recurrences; modulo optimization problems and integer linear programming; equivalent forms of zero-one programs; and number theoretic foundations of finite precision arithmetic. This monograph will be of interest to students and practitioners in the field of applied mathematics.
Theoretical Numerical Analysis
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Author : Kendall Atkinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-07
Theoretical Numerical Analysis written by Kendall Atkinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-07 with Mathematics categories.
Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scienti?c disciplines and a resurgence of interest in the modern as well as the cl- sical techniques of applied mathematics. This renewal of interest, both in research and teaching, has led to the establishment of the series: Texts in Applied Mathematics (TAM). Thedevelopmentofnewcoursesisanaturalconsequenceofahighlevelof excitement on the research frontier as newer techniques, such as numerical and symbolic computer systems, dynamical systems, and chaos, mix with and reinforce the traditional methods of applied mathematics. Thus, the purpose of this textbook series is to meet the current and future needs of these advances and to encourage the teaching of new courses. TAM will publish textbooks suitable for use in advanced undergraduate and beginning graduate courses, and will complement the Applied Ma- ematical Sciences (AMS) series, which will focus on advanced textbooks and research-level monographs.
Numerical Analysis Of Spectral Methods
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Author : David Gottlieb
language : en
Publisher: SIAM
Release Date : 1977-01-01
Numerical Analysis Of Spectral Methods written by David Gottlieb and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977-01-01 with Technology & Engineering categories.
A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis.