The Birth Of Numerical Analysis

Author : Adhemar Bultheel,Ronald Cools
Publisher : World Scientific
Page : 240 pages
File Size : 52,7 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812836267

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The Birth of Numerical Analysis by Adhemar Bultheel,Ronald Cools Pdf

The 1947 paper by John von Neumann and Herman Goldstine, OC Numerical Inverting of Matrices of High OrderOCO ( Bulletin of the AMS, Nov. 1947), is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book is a unique collection of contributions by researchers who have lived through this evolution, testifying about their personal experiences and sketching the evolution of their respective subdomains since the early years. Sample Chapter(s). Chapter 1: Some pioneers of extrapolation methods (323 KB). Contents: Some Pioneers of Extrapolation Methods (C Brezinski); Very Basic Multidimensional Extrapolation Quadrature (J N Lyness); Numerical Methods for Ordinary Differential Equations: Early Days (J C Butcher); Interview with Herbert Bishop Keller (H M Osinga); A Personal Perspective on the History of the Numerical Analysis of Fredholm Integral Equations of the Second Kind (K Atkinson); Memoires on Building on General Purpose Numerical Algorithms Library (B Ford); Recent Trends in High Performance Computing (J J Dongarra et al.); Nonnegativity Constraints in Numerical Analysis (D-H Chen & R J Plemmons); On Nonlinear Optimization Since 1959 (M J D Powell); The History and Development of Numerical Analysis in Scotland: A Personal Perspective (G Alistair Watson); Remembering Philip Rabinowitz (P J Davis & A S Fraenkel); My Early Experiences with Scientific Computation (P J Davis); Applications of Chebyshev Polynomials: From Theoretical Kinematics to Practical Computations (R Piessens). Readership: Mathematicians in numerical analysis and mathematicians who are interested in the history of mathematics.

Author : H. H. Goldstine
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494723

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A History of Numerical Analysis from the 16th through the 19th Century by H. H. Goldstine Pdf

In this book I have attempted to trace the development of numerical analysis during the period in which the foundations of the modern theory were being laid. To do this I have had to exercise a certain amount of selectivity in choosing and in rejecting both authors and papers. I have rather arbitrarily chosen, in the main, the most famous mathematicians of the period in question and have concentrated on their major works in numerical analysis at the expense, perhaps, of other lesser known but capable analysts. This selectivity results from the need to choose from a large body of literature, and from my feeling that almost by definition the great masters of mathematics were the ones responsible for the most significant accomplishments. In any event I must accept full responsibility for the choices. I would particularly like to acknowledge my thanks to Professor Otto Neugebauer for his help and inspiration in the preparation of this book. This consisted of many friendly discussions that I will always value. I should also like to express my deep appreciation to the International Business Machines Corporation of which I have the honor of being a Fellow and in particular to Dr. Ralph E. Gomory, its Vice-President for Research, for permitting me to undertake the writing of this book and for helping make it possible by his continuing encouragement and support.

Author : C. Brezinski,L. Wuytack
Publisher : Elsevier
Page : 512 pages
File Size : 47,8 Mb
Release : 2012-12-02
Category : Mathematics
ISBN : 9780444598585

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Numerical Analysis: Historical Developments in the 20th Century by C. Brezinski,L. Wuytack Pdf

Numerical analysis has witnessed many significant developments in the 20th century. This book brings together 16 papers dealing with historical developments, survey papers and papers on recent trends in selected areas of numerical analysis, such as: approximation and interpolation, solution of linear systems and eigenvalue problems, iterative methods, quadrature rules, solution of ordinary-, partial- and integral equations. The papers are reprinted from the 7-volume project of the Journal of Computational and Applied Mathematics on '/homepage/sac/cam/na2000/index.htmlNumerical Analysis 2000'. An introductory survey paper deals with the history of the first courses on numerical analysis in several countries and with the landmarks in the development of important algorithms and concepts in the field.

Author : Walter Gautschi
Publisher : Springer Science & Business Media
Page : 611 pages
File Size : 50,8 Mb
Release : 2011-12-06
Category : Mathematics
ISBN : 9780817682590

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Numerical Analysis by Walter Gautschi Pdf

Revised and updated, this second edition of Walter Gautschi's successful Numerical Analysis explores computational methods for problems arising in the areas of classical analysis, approximation theory, and ordinary differential equations, among others. Topics included in the book are presented with a view toward stressing basic principles and maintaining simplicity and teachability as far as possible, while subjects requiring a higher level of technicality are referenced in detailed bibliographic notes at the end of each chapter. Readers are thus given the guidance and opportunity to pursue advanced modern topics in more depth. Along with updated references, new biographical notes, and enhanced notational clarity, this second edition includes the expansion of an already large collection of exercises and assignments, both the kind that deal with theoretical and practical aspects of the subject and those requiring machine computation and the use of mathematical software. Perhaps most notably, the edition also comes with a complete solutions manual, carefully developed and polished by the author, which will serve as an exceptionally valuable resource for instructors.

Author : J. Stoer,R. Bulirsch
Publisher : Springer Science & Business Media
Page : 674 pages
File Size : 47,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475722727

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Introduction to Numerical Analysis by J. Stoer,R. Bulirsch Pdf

On the occasion of this new edition, the text was enlarged by several new sections. Two sections on B-splines and their computation were added to the chapter on spline functions: Due to their special properties, their flexibility, and the availability of well-tested programs for their computation, B-splines play an important role in many applications. Also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. Even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. We will explain some of these techniques in connection with the Cholesky algorithm for solving positive definite linear systems. The chapter on eigenvalue problems was enlarged by a section on the Lanczos algorithm; the sections on the LR and QR algorithm were rewritten and now contain a description of implicit shift techniques. In order to some extent take into account the progress in the area of ordinary differential equations, a new section on implicit differential equa tions and differential-algebraic systems was added, and the section on stiff differential equations was updated by describing further methods to solve such equations.

Author : Endre Süli,David F. Mayers
Publisher : Cambridge University Press
Page : 440 pages
File Size : 46,5 Mb
Release : 2003-08-28
Category : Mathematics
ISBN : 0521007941

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An Introduction to Numerical Analysis by Endre Süli,David F. Mayers Pdf

An introduction to numerical analysis combining rigour with practical applications, and providing numerous exercises plus solutions.

Author : Walter Gautschi
Publisher : Springer Science & Business Media
Page : 524 pages
File Size : 47,7 Mb
Release : 1997-08-19
Category : Mathematics
ISBN : 9780817638955

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Numerical Analysis by Walter Gautschi Pdf

Author : Arieh Iserles
Publisher : Cambridge University Press
Page : 481 pages
File Size : 41,6 Mb
Release : 2008-11-27
Category : Mathematics
ISBN : 9781139473767

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A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles Pdf

Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This second edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems.

Author : Victor S. Ryaben'kii,Semyon V. Tsynkov
Publisher : CRC Press
Page : 552 pages
File Size : 47,7 Mb
Release : 2006-11-02
Category : Mathematics
ISBN : 9781420011166

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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 : Larkin Ridgway Scott
Publisher : Princeton University Press
Page : 342 pages
File Size : 46,8 Mb
Release : 2011-04-18
Category : Mathematics
ISBN : 9781400838967

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Numerical Analysis by Larkin Ridgway Scott Pdf

Computational science is fundamentally changing how technological questions are addressed. The design of aircraft, automobiles, and even racing sailboats is now done by computational simulation. The mathematical foundation of this new approach is numerical analysis, which studies algorithms for computing expressions defined with real numbers. Emphasizing the theory behind the computation, this book provides a rigorous and self-contained introduction to numerical analysis and presents the advanced mathematics that underpin industrial software, including complete details that are missing from most textbooks. Using an inquiry-based learning approach, Numerical Analysis is written in a narrative style, provides historical background, and includes many of the proofs and technical details in exercises. Students will be able to go beyond an elementary understanding of numerical simulation and develop deep insights into the foundations of the subject. They will no longer have to accept the mathematical gaps that exist in current textbooks. For example, both necessary and sufficient conditions for convergence of basic iterative methods are covered, and proofs are given in full generality, not just based on special cases. The book is accessible to undergraduate mathematics majors as well as computational scientists wanting to learn the foundations of the subject. Presents the mathematical foundations of numerical analysis Explains the mathematical details behind simulation software Introduces many advanced concepts in modern analysis Self-contained and mathematically rigorous Contains problems and solutions in each chapter Excellent follow-up course to Principles of Mathematical Analysis by Rudin

Author : Timo Heister,Leo G. Rebholz,Fei Xue
Publisher : Walter de Gruyter GmbH & Co KG
Page : 193 pages
File Size : 41,9 Mb
Release : 2019-03-18
Category : Mathematics
ISBN : 9783110573329

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Numerical Analysis by Timo Heister,Leo G. Rebholz,Fei Xue Pdf

Numerical analysis deals with the development and analysis of algorithms for scientific computing, and is in itself a very important part of mathematics, which has become more and more prevalent across the mathematical spectrum. This book is an introduction to numerical methods for solving linear and nonlinear systems of equations as well as ordinary and partial differential equations, and for approximating curves, functions, and integrals.

Author : Jeffery J. Leader
Publisher : Addison-Wesley
Page : 590 pages
File Size : 45,5 Mb
Release : 2004
Category : Numerical analysis
ISBN : 0321223357

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Numerical Analysis and Scientific Computation by Jeffery J. Leader Pdf

This text is intended for a first course in Numerical Analysis taken by students majoring in mathematics, engineering, computer science, and the sciences. This text emphasizes the mathematical ideas behind the methods and the idea of mixing methods for robustness. The optional use of MATLAB is incorporated throughout the text.

Author : Herbert B. Keller
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 46,9 Mb
Release : 2018-11-14
Category : Mathematics
ISBN : 9780486828343

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Numerical Methods for Two-Point Boundary-Value Problems by Herbert B. Keller Pdf

Elementary yet rigorous, this concise treatment is directed toward students with a knowledge of advanced calculus, basic numerical analysis, and some background in ordinary differential equations and linear algebra. 1968 edition.

Author : Anthony Ralston,Philip Rabinowitz
Publisher : Courier Corporation
Page : 644 pages
File Size : 53,5 Mb
Release : 2001-01-01
Category : Mathematics
ISBN : 048641454X

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A First Course in Numerical Analysis by Anthony Ralston,Philip Rabinowitz Pdf

Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.

Author : A. C. Faul
Publisher : CRC Press
Page : 292 pages
File Size : 47,6 Mb
Release : 2016-03-23
Category : Mathematics
ISBN : 9781498712194

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A Concise Introduction to Numerical Analysis by A. C. Faul Pdf

This textbook provides an accessible and concise introduction to numerical analysis for upper undergraduate and beginning graduate students from various backgrounds. It was developed from the lecture notes of four successful courses on numerical analysis taught within the MPhil of Scientific Computing at the University of Cambridge. The book is easily accessible, even to those with limited knowledge of mathematics. Students will get a concise, but thorough introduction to numerical analysis. In addition the algorithmic principles are emphasized to encourage a deeper understanding of why an algorithm is suitable, and sometimes unsuitable, for a particular problem. A Concise Introduction to Numerical Analysis strikes a balance between being mathematically comprehensive, but not overwhelming with mathematical detail. In some places where further detail was felt to be out of scope of the book, the reader is referred to further reading. The book uses MATLAB® implementations to demonstrate the workings of the method and thus MATLAB's own implementations are avoided, unless they are used as building blocks of an algorithm. In some cases the listings are printed in the book, but all are available online on the book’s page at www.crcpress.com. Most implementations are in the form of functions returning the outcome of the algorithm. Also, examples for the use of the functions are given. Exercises are included in line with the text where appropriate, and each chapter ends with a selection of revision exercises. Solutions to odd-numbered exercises are also provided on the book’s page at www.crcpress.com. This textbook is also an ideal resource for graduate students coming from other subjects who will use numerical techniques extensively in their graduate studies.