Theoretical Numerical Analysis

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 576 pages
File Size : 51,5 Mb
Release : 2007-06-07
Category : Mathematics
ISBN : 9780387287690

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Theoretical Numerical Analysis by Kendall Atkinson,Weimin Han Pdf

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.

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 466 pages
File Size : 42,5 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387215266

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Theoretical Numerical Analysis by Kendall Atkinson,Weimin Han Pdf

This book gives an introduction to functional analysis in a way that is tailored to fit the needs of the researcher or student. The book explains the basic results of functional analysis as well as relevant topics in numerical analysis. Applications of functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. The material is especially useful for researchers and students who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this book.

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 47,7 Mb
Release : 2001-03-09
Category : Mathematics
ISBN : 9780387951423

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Theoretical Numerical Analysis by Kendall Atkinson,Weimin Han Pdf

This book gives an introduction to functional analysis in a way that is tailored to fit the needs of the researcher or student. The book explains the basic results of functional analysis as well as relevant topics in numerical analysis. Applications of functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. The material is especially useful for researchers and students who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this book.

Author : Burton Wendroff
Publisher : Elsevier
Page : 252 pages
File Size : 43,7 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483275222

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Theoretical Numerical Analysis by Burton Wendroff Pdf

Theoretical Numerical Analysis focuses on the presentation of numerical analysis as a legitimate branch of mathematics. The publication first elaborates on interpolation and quadrature and approximation. Discussions focus on the degree of approximation by polynomials, Chebyshev approximation, orthogonal polynomials and Gaussian quadrature, approximation by interpolation, nonanalytic interpolation and associated quadrature, and Hermite interpolation. The text then ponders on ordinary differential equations and solutions of equations. Topics include iterative methods for nonlinear systems, matrix eigenvalue problems, matrix inversion by triangular decomposition, homogeneous boundary value problems, and initial value problems. The publication takes a look at partial differential equations, including heat equation, stability, maximum principle, and first order systems. The manuscript is a vital source of data for mathematicians and researchers interested in theoretical numerical analysis.

Author : Kendall Atkinson,Weimin Han
Publisher : Springer Science & Business Media
Page : 631 pages
File Size : 54,6 Mb
Release : 2009-06-12
Category : Mathematics
ISBN : 9781441904584

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Theoretical Numerical Analysis by Kendall Atkinson,Weimin Han Pdf

This textbook prepares graduate students for research in numerical analysis/computational mathematics by giving to them a mathematical framework embedded in functional analysis and focused on numerical analysis. This helps the student to move rapidly into a research program. The text covers basic results of functional analysis, approximation theory, Fourier analysis and wavelets, iteration methods for nonlinear equations, finite difference methods, Sobolev spaces and weak formulations of boundary value problems, finite element methods, elliptic variational inequalities and their numerical solution, numerical methods for solving integral equations of the second kind, and boundary integral equations for planar regions. The presentation of each topic is meant to be an introduction with certain degree of depth. Comprehensive references on a particular topic are listed at the end of each chapter for further reading and study. Because of the relevance in solving real world problems, multivariable polynomials are playing an ever more important role in research and applications. In this third editon, a new chapter on this topic has been included and some major changes are made on two chapters from the previous edition. In addition, there are numerous minor changes throughout the entire text and new exercises are added. Review of earlier edition: "...the book is clearly written, quite pleasant to read, and contains a lot of important material; and the authors have done an excellent job at balancing theoretical developments, interesting examples and exercises, numerical experiments, and bibliographical references." R. Glowinski, SIAM Review, 2003

Author : G. M. Phillips,Peter J. Taylor
Publisher : Elsevier
Page : 447 pages
File Size : 40,8 Mb
Release : 1996-07-05
Category : Mathematics
ISBN : 9780080519128

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Theory and Applications of Numerical Analysis by G. M. Phillips,Peter J. Taylor Pdf

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

Author : Peter Linz
Publisher : Courier Dover Publications
Page : 242 pages
File Size : 50,7 Mb
Release : 2019-06-12
Category : Mathematics
ISBN : 9780486840901

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Theoretical Numerical Analysis by Peter Linz Pdf

This concise text introduces numerical analysis as a practical, problem-solving discipline. The three-part presentation begins with the fundamentals of functional analysis and approximation theory. Part II outlines the major results of theoretical numerical analysis, reviewing product integration, approximate expansion methods, the minimization of functions, and related topics. Part III considers specific subjects that illustrate the power and usefulness of theoretical analysis. Ideal as a text for a one-year graduate course, the book also offers engineers and scientists experienced in numerical computing a simple introduction to the major ideas of modern numerical analysis. Some practical experience with computational mathematics and the ability to relate this experience to new concepts is assumed. Otherwise, no background beyond advanced calculus is presupposed. Moreover, the ideas of functional analysis used throughout the text are introduced and developed only to the extent they are needed.

Author : Anonim
Publisher : Unknown
Page : 625 pages
File Size : 51,7 Mb
Release : 2009
Category : Functional analysis
ISBN : 7510052785

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Theoretical Numerical Analysis by Anonim Pdf

Author : Victor S. Ryaben'kii,Semyon V. Tsynkov
Publisher : CRC Press
Page : 564 pages
File Size : 50,5 Mb
Release : 2006-11-02
Category : Mathematics
ISBN : 9781000738285

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A Theoretical Introduction to Numerical Analysis by Victor S. Ryaben'kii,Semyon V. Tsynkov Pdf

A Theoretical Introduction to Numerical Analysis presents the general methodology and principles of numerical analysis, illustrating these concepts using numerical methods from real analysis, linear algebra, and differential equations. The book focuses on how to efficiently represent mathematical models for computer-based study. An access

Author : L.-K. Hua,Y. Wang
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 55,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642678295

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Applications of Number Theory to Numerical Analysis by L.-K. Hua,Y. Wang Pdf

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.

Author : Brian Sutton
Publisher : SIAM
Page : 431 pages
File Size : 48,8 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781611975703

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Numerical Analysis by Brian Sutton Pdf

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.

Author : Azmy S. Ackleh,Edward James Allen,R. Baker Kearfott,Padmanabhan Seshaiyer
Publisher : CRC Press
Page : 628 pages
File Size : 47,5 Mb
Release : 2009-07-20
Category : Mathematics
ISBN : 9781420091588

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Classical and Modern Numerical Analysis by Azmy S. Ackleh,Edward James Allen,R. Baker Kearfott,Padmanabhan Seshaiyer Pdf

Classical and Modern Numerical Analysis: Theory, Methods and Practice provides a sound foundation in numerical analysis for more specialized topics, such as finite element theory, advanced numerical linear algebra, and optimization. It prepares graduate students for taking doctoral examinations in numerical analysis.The text covers the main areas o

Author : R. S. Varga
Publisher : SIAM
Page : 81 pages
File Size : 45,8 Mb
Release : 1971-01-01
Category : Mathematics
ISBN : 9780898710038

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Functional Analysis and Approximation Theory in Numerical Analysis by R. S. Varga Pdf

Surveys the enormous literature on numerical approximation of solutions of elliptic boundary problems by means of variational and finite element methods, requiring almost constant application of results and techniques from functional analysis and approximation theory to the field of numerical analysis.

Author : Weimin Han,B. Daya Reddy
Publisher : Springer Science & Business Media
Page : 428 pages
File Size : 46,7 Mb
Release : 2012-11-19
Category : Mathematics
ISBN : 9781461459408

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Plasticity by Weimin Han,B. Daya Reddy Pdf

This book focuses on the theoretical aspects of small strain theory of elastoplasticity with hardening assumptions. It provides a comprehensive and unified treatment of the mathematical theory and numerical analysis. It is divided into three parts, with the first part providing a detailed introduction to plasticity, the second part covering the mathematical analysis of the elasticity problem, and the third part devoted to error analysis of various semi-discrete and fully discrete approximations for variational formulations of the elastoplasticity. This revised and expanded edition includes material on single-crystal and strain-gradient plasticity. In addition, the entire book has been revised to make it more accessible to readers who are actively involved in computations but less so in numerical analysis. Reviews of earlier edition: “The authors have written an excellent book which can be recommended for specialists in plasticity who wish to know more about the mathematical theory, as well as those with a background in the mathematical sciences who seek a self-contained account of the mechanics and mathematics of plasticity theory.” (ZAMM, 2002) “In summary, the book represents an impressive comprehensive overview of the mathematical approach to the theory and numerics of plasticity. Scientists as well as lecturers and graduate students will find the book very useful as a reference for research or for preparing courses in this field.” (Technische Mechanik) "The book is professionally written and will be a useful reference to researchers and students interested in mathematical and numerical problems of plasticity. It represents a major contribution in the area of continuum mechanics and numerical analysis." (Math Reviews)

Author : Massimo Fornasier
Publisher : Walter de Gruyter
Page : 351 pages
File Size : 55,6 Mb
Release : 2010-07-30
Category : Mathematics
ISBN : 9783110226157

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Theoretical Foundations and Numerical Methods for Sparse Recovery by Massimo Fornasier Pdf

The present collection is the very first contribution of this type in the field of sparse recovery. Compressed sensing is one of the important facets of the broader concept presented in the book, which by now has made connections with other branches such as mathematical imaging, inverse problems, numerical analysis and simulation. The book consists of four lecture notes of courses given at the Summer School on "Theoretical Foundations and Numerical Methods for Sparse Recovery" held at the Johann Radon Institute for Computational and Applied Mathematics in Linz, Austria, in September 2009. This unique collection will be of value for a broad community and may serve as a textbook for graduate courses. From the contents: "Compressive Sensing and Structured Random Matrices" by Holger Rauhut "Numerical Methods for Sparse Recovery" by Massimo Fornasier "Sparse Recovery in Inverse Problems" by Ronny Ramlau and Gerd Teschke "An Introduction to Total Variation for Image Analysis" by Antonin Chambolle, Vicent Caselles, Daniel Cremers, Matteo Novaga and Thomas Pock