A History Of Numerical Analysis From The 16th Through The 19th Century

Author : H. H. Goldstine
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 40,5 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 : Herman Heine Goldstine
Publisher : Unknown
Page : 128 pages
File Size : 54,6 Mb
Release : 1977
Category : Electronic
ISBN : OCLC:646169575

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A history of numerical analysis from the 16th through the 19th century by Herman Heine Goldstine Pdf

Author : C. Brezinski,L. Wuytack
Publisher : Elsevier
Page : 512 pages
File Size : 46,9 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 : Mehiddin Al-Baali,Anton Purnama,Lucio Grandinetti
Publisher : Springer Nature
Page : 307 pages
File Size : 47,8 Mb
Release : 2021-12-01
Category : Mathematics
ISBN : 9783030720407

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Numerical Analysis and Optimization by Mehiddin Al-Baali,Anton Purnama,Lucio Grandinetti Pdf

This book gathers selected, peer-reviewed contributions presented at the Fifth International Conference on Numerical Analysis and Optimization (NAO-V), which was held at Sultan Qaboos University, Oman, on January 6-9, 2020. Each chapter reports on developments in key fields, such as numerical analysis, numerical optimization, numerical linear algebra, numerical differential equations, optimal control, approximation theory, applied mathematics, derivative-free optimization methods, programming models, and challenging applications that frequently arise in statistics, econometrics, finance, physics, medicine, biology, engineering and industry. Many real-world, complex problems can be formulated as optimization tasks, and can be characterized further as large scale, unconstrained, constrained, non-convex, nondifferentiable or discontinuous, and therefore require adequate computational methods, algorithms and software tools. These same tools are often employed by researchers working in current IT hot topics, such as big data, optimization and other complex numerical algorithms in the cloud, devising special techniques for supercomputing systems. This interdisciplinary view permeates the work included in this volume. The NAO conference series is held every three years at Sultan Qaboos University, with the aim of bringing together a group of international experts and presenting novel and advanced applications to facilitate interdisciplinary studies among pure scientific and applied knowledge. It is a venue where prominent scientists gather to share innovative ideas and know-how relating to new scientific methodologies, to promote scientific exchange, to discuss possible future cooperations, and to promote the mobility of local and young researchers.

Author : Naser Mahdavi Tabatabaei,Nicu Bizon
Publisher : Springer Nature
Page : 1033 pages
File Size : 45,7 Mb
Release : 2021-03-22
Category : Technology & Engineering
ISBN : 9783030621919

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Numerical Methods for Energy Applications by Naser Mahdavi Tabatabaei,Nicu Bizon Pdf

This book provides a thorough guide to the use of numerical methods in energy systems and applications. It presents methods for analysing engineering applications for energy systems, discussing finite difference, finite element, and other advanced numerical methods. Solutions to technical problems relating the application of these methods to energy systems are also thoroughly explored. Readers will discover diverse perspectives of the contributing authors and extensive discussions of issues including: • a wide variety of numerical methods concepts and related energy systems applications;• systems equations and optimization, partial differential equations, and finite difference method;• methods for solving nonlinear equations, special methods, and their mathematical implementation in multi-energy sources;• numerical investigations of electrochemical fields and devices; and• issues related to numerical approaches and optimal integration of energy consumption. This is a highly informative and carefully presented book, providing scientific and academic insight for readers with an interest in numerical methods and energy systems.

Author : James F. Epperson
Publisher : John Wiley & Sons
Page : 614 pages
File Size : 50,8 Mb
Release : 2013-10-07
Category : Mathematics
ISBN : 9781118367599

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An Introduction to Numerical Methods and Analysis by James F. Epperson Pdf

Praise for the First Edition ". . . outstandingly appealing with regard to its style, contents, considerations of requirements of practice, choice of examples, and exercises."—Zentralblatt MATH ". . . carefully structured with many detailed worked examples."—The Mathematical Gazette The Second Edition of the highly regarded An Introduction to Numerical Methods and Analysis provides a fully revised guide to numerical approximation. The book continues to be accessible and expertly guides readers through the many available techniques of numerical methods and analysis. An Introduction to Numerical Methods and Analysis, Second Edition reflects the latest trends in the field, includes new material and revised exercises, and offers a unique emphasis on applications. The author clearly explains how to both construct and evaluate approximations for accuracy and performance, which are key skills in a variety of fields. A wide range of higher-level methods and solutions, including new topics such as the roots of polynomials, spectral collocation, finite element ideas, and Clenshaw-Curtis quadrature, are presented from an introductory perspective, and the Second Edition also features: Chapters and sections that begin with basic, elementary material followed by gradual coverage of more advanced material Exercises ranging from simple hand computations to challenging derivations and minor proofs to programming exercises Widespread exposure and utilization of MATLAB An appendix that contains proofs of various theorems and other material The book is an ideal textbook for students in advanced undergraduate mathematics and engineering courses who are interested in gaining an understanding of numerical methods and numerical analysis.

Author : John Todd
Publisher : Academic Press
Page : 254 pages
File Size : 51,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483268910

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Numerical Analysis by John Todd Pdf

Basic Numerical Mathematics, Volume 1: Numerical Analysis focuses on numerical analysis, with emphasis on the ideas of "controlled computational experiments" and "bad examples". The concepts of convergence and continuity are discussed, along with the rate of convergence, acceleration, and asymptotic series. The more traditional topics of interpolation, quadrature, and differential equations are also explored. Comprised of 10 chapters, this volume begins with an analysis of the algorithms of Gauss, Borchardt, and Carlson in relation to the rate of convergence. The reader is then introduced to orders of magnitude and rates of convergence; recurrence relations for powers; and the solution of equations. Subsequent chapters deal with uniform convergence and approximation; the acceleration processes of Aitken and Euler; asymptotic series; interpolation; and quadrature. The final chapter is devoted to linear difference equations with constant coefficients, along with differentiation and differential equations. This book will be of interest to mathematicians and students of mathematics.

Author : Brian Sutton
Publisher : SIAM
Page : 448 pages
File Size : 52,6 Mb
Release : 2019-04-18
Category : Mathematics
ISBN : 9781611975697

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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 : Adhemar Bultheel,Ronald Cools
Publisher : World Scientific
Page : 240 pages
File Size : 44,8 Mb
Release : 2010
Category : Mathematics
ISBN : 9789812836250

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

The 1947 paper by John von Neumann & Herman Goldstine, 'Numerical Inverting of Matrices of High Order', is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book collects contributions by researchers who have lived through this evolution.

Author : Kendall Atkinson
Publisher : John Wiley & Sons
Page : 726 pages
File Size : 52,5 Mb
Release : 1991-01-16
Category : Mathematics
ISBN : 9780471624899

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An Introduction to Numerical Analysis by Kendall Atkinson Pdf

This Second Edition of a standard numerical analysis text retains organization of the original edition, but all sections have been revised, some extensively, and bibliographies have been updated. New topics covered include optimization, trigonometric interpolation and the fast Fourier transform, numerical differentiation, the method of lines, boundary value problems, the conjugate gradient method, and the least squares solutions of systems of linear equations. Contains many problems, some with solutions.

Author : Walter Gautschi
Publisher : Springer Science & Business Media
Page : 611 pages
File Size : 45,5 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 : David Kincaid,David Ronald Kincaid,Elliott Ward Cheney
Publisher : American Mathematical Soc.
Page : 810 pages
File Size : 43,9 Mb
Release : 2009
Category : Numerical analysis
ISBN : 9780821847886

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Numerical Analysis by David Kincaid,David Ronald Kincaid,Elliott Ward Cheney Pdf

This book introduces students with diverse backgrounds to various types of mathematical analysis that are commonly needed in scientific computing. The subject of numerical analysis is treated from a mathematical point of view, offering a complete analysis of methods for scientific computing with appropriate motivations and careful proofs. In an engaging and informal style, the authors demonstrate that many computational procedures and intriguing questions of computer science arise from theorems and proofs. Algorithms are presented in pseudocode, so that students can immediately write computer programs in standard languages or use interactive mathematical software packages. This book occasionally touches upon more advanced topics that are not usually contained in standard textbooks at this level.

Author : Santosh K Gupta
Publisher : New Age International
Page : 426 pages
File Size : 54,6 Mb
Release : 1995
Category : Differential quations
ISBN : 8122406513

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Numerical Methods for Engineers by Santosh K Gupta Pdf

This Book Is Intended To Be A Text For Either A First Or A Second Course In Numerical Methods For Students In All Engineering Disciplines. Difficult Concepts, Which Usually Pose Problems To Students Are Explained In Detail And Illustrated With Solved Examples. Enough Elementary Material That Could Be Covered In The First-Level Course Is Included, For Example, Methods For Solving Linear And Nonlinear Algebraic Equations, Interpolation, Differentiation, Integration, And Simple Techniques For Integrating Odes And Pdes (Ordinary And Partial Differential Equations).Advanced Techniques And Concepts That Could Form Part Of A Second-Level Course Includegears Method For Solving Ode-Ivps (Initial Value Problems), Stiffness Of Ode- Ivps, Multiplicity Of Solutions, Convergence Characteristics, The Orthogonal Collocation Method For Solving Ode-Bvps (Boundary Value Problems) And Finite Element Techniques. An Extensive Set Of Graded Problems, Often With Hints, Has Been Included.Some Involve Simple Applications Of The Concepts And Can Be Solved Using A Calculator, While Several Are From Real-Life Situations And Require Writing Computer Programs Or Use Of Library Subroutines. Practice On These Is Expected To Build Up The Reader'S Confidence In Developing Large Computer Codes.

Author : Kristine K. Fowler
Publisher : CRC Press
Page : 412 pages
File Size : 49,9 Mb
Release : 2004-05-25
Category : Language Arts & Disciplines
ISBN : 0824750357

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Using the Mathematics Literature by Kristine K. Fowler Pdf

This reference serves as a reader-friendly guide to every basic tool and skill required in the mathematical library and helps mathematicians find resources in any format in the mathematics literature. It lists a wide range of standard texts, journals, review articles, newsgroups, and Internet and database tools for every major subfield in mathematics and details methods of access to primary literature sources of new research, applications, results, and techniques. Using the Mathematics Literature is the most comprehensive and up-to-date resource on mathematics literature in both print and electronic formats, presenting time-saving strategies for retrieval of the latest information.

Author : Larkin Ridgway Scott
Publisher : Princeton University Press
Page : 342 pages
File Size : 40,8 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