Numerical Analysis

Numerical Analysis
Available:
Author: Rainer Kress
Pages: 326
ISBN: 9781461205999
Release: 2012-12-06
Editor: Springer Science & Business Media

DESCRIPTION OF THE BOOK:

An introduction into numerical analysis for students in mathematics, physics, and engineering. Instead of attempting to exhaustively cover everything, the goal is to guide readers towards the basic ideas and general principles by way of the main and important numerical methods. The book includes the necessary basic functional analytic tools for the solid mathematical foundation of numerical analysis -- indispensable for any deeper study and understanding of numerical methods, in particular, for differential equations and integral equations. The text is presented in a concise and easily understandable fashion so as to be successfully mastered in a one-year course.

Analysis of Numerical Methods

Analysis of Numerical Methods
Available:
Author: Eugene Isaacson,Herbert Bishop Keller
Pages: 576
ISBN: 9780486137988
Release: 2012-04-26
Editor: Courier Corporation

DESCRIPTION OF THE BOOK:

This excellent text for advanced undergraduate and graduate students covers norms, numerical solutions of linear systems and matrix factoring, eigenvalues and eigenvectors, polynomial approximation, and more. Many examples and problems. 1966 edition.

Numerical Analysis

Numerical Analysis
Available:
Author: L. Ridgway Scott
Pages: 344
ISBN: 1400838967
Release: 2011-04-18
Editor: Princeton University Press

DESCRIPTION OF THE BOOK:

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

Numerical Analysis for Statisticians

Numerical Analysis for Statisticians
Available:
Author: Kenneth Lange
Pages: 600
ISBN: 9781441959447
Release: 2010-06-15
Editor: Springer Science & Business Media

DESCRIPTION OF THE BOOK:

Numerical analysis is the study of computation and its accuracy, stability and often its implementation on a computer. This book focuses on the principles of numerical analysis and is intended to equip those readers who use statistics to craft their own software and to understand the advantages and disadvantages of different numerical methods.

Numerical Analysis

Numerical Analysis
Available:
Author: David Ronald Kincaid,Elliott Ward Cheney
Pages: 788
ISBN: 9780821847886
Release: 2002
Editor: American Mathematical Soc.

DESCRIPTION OF THE BOOK:

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.

Principles and Procedures of Numerical Analysis

Principles and Procedures of Numerical Analysis
Available:
Author: Ferenc Szidarovszky,Sidney J. Yakowitz
Pages: 331
ISBN: 9781489927507
Release: 2013-11-11
Editor: Springer

DESCRIPTION OF THE BOOK:

It is an incontestable fact that numerical analysis techniques are used rou tinely (although not always effectively) in virtually every quantitative field of scientific endeavor. In this book, which is directed toward upper-division and graduate level students in engineering and mathematics, we have selected for discussion subjects that are traditionally found in numerical analysis texts. But our choice of methodology rejects the traditional where analysis and experience clearly warrant such a departure, and one of our primary aspirations in this work is to equip the reader with the wherewithal to apply numerical analysis thinking to nontraditional subjects. For there is a plethora of computer-oriented sciences such as optimization, statistics, and system analysis and identification that are sorely in need of methods comparable to those related here for classical numerical analysis problems. Toward uncovering for the reader the structure of numerical methods we have, for example, devoted a chapter to a metric space theory for iter ative application of operators. In this chapter, we have collected those definitions and concepts of real and functional analysis that are requisite to a modern intermediate-level exposition of the principles of numerical anal ysis. Further, we derive the abstract theory (most notably, the contraction mapping theorem) for iteration processes.

A Concise Introduction to Numerical Analysis

A Concise Introduction to Numerical Analysis
Available:
Author: A. C. Faul
Pages: 292
ISBN: 9781498712217
Release: 2018-10-24
Editor: CRC Press

DESCRIPTION OF THE BOOK:

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.

INTRODUCTORY METHODS OF NUMERICAL ANALYSIS

INTRODUCTORY METHODS OF NUMERICAL ANALYSIS
Available:
Author: S. S. SASTRY
Pages: 464
ISBN: 9788120345928
Release: 2012-06-12
Editor: PHI Learning Pvt. Ltd.

DESCRIPTION OF THE BOOK:

This thoroughly revised and updated text, now in its fifth edition, continues to provide a rigorous introduction to the fundamentals of numerical methods required in scientific and technological applications, emphasizing on teaching students numerical methods and in helping them to develop problem-solving skills. While the essential features of the previous editions such as References to MATLAB, IMSL, Numerical Recipes program libraries for implementing the numerical methods are retained, a chapter on Spline Functions has been added in this edition because of their increasing importance in applications. This text is designed for undergraduate students of all branches of engineering. NEW TO THIS EDITION : Includes additional modified illustrative examples and problems in every chapter. Provides answers to all chapter-end exercises. Illustrates algorithms, computational steps or flow charts for many numerical methods. Contains four model question papers at the end of the text.

Theory and Applications of Numerical Analysis

Theory and Applications of Numerical Analysis
Available:
Author: G. M. Phillips,Peter J. Taylor
Pages: 447
ISBN: 0080519121
Release: 1996-07-05
Editor: Elsevier

DESCRIPTION OF THE BOOK:

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 1993

Numerical Analysis 1993
Available:
Author: D.F. Griffiths,G.A. Watson
Pages: 292
ISBN: 9781000158052
Release: 2020-10-08
Editor: CRC Press

DESCRIPTION OF THE BOOK:

This volume contains invited papers presented at the 15th Dundee Biennial Conference on Numerical Analysis held at the University of Dundee in June of 1993. The Dundee Conferences are important events in the numerical analysis calendar, and the papers published here represent accounts of recent research work by leading numerical analysts covering a wide range of fields of interest. The book is a valuable guide to the direction of current research in many areas of numerical analysis. It will be of particular interest to graduate students and research workers concerned with the theory and application of numerical methods for solving ordinary and partial differential equations.

A Theoretical Introduction to Numerical Analysis

A Theoretical Introduction to Numerical Analysis
Available:
Author: Victor S. Ryaben'kii,Semyon V. Tsynkov
Pages: 552
ISBN: 9781000738285
Release: 2006-11-02
Editor: CRC Press

DESCRIPTION OF THE BOOK:

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

Topics in Numerical Analysis

Topics in Numerical Analysis
Available:
Author: G. Alefeld,Xiaojun Chen
Pages: 249
ISBN: UOM:39015054260297
Release: 2001-09-11
Editor: Springer Science & Business Media

DESCRIPTION OF THE BOOK:

This collection of papers on numerical analysis with special emphasis on nonlinear problems covers a broad spectrum of fields. Several papers are involved in applying numerical methods for proving the existence of solutions of nonlinear problems, e.g. of boundary problems or of obstacle problems. Naturally the solution of linear and nonlinear problems by iterative methods is the subject of a couple of papers. Here topics like the fast verification of solutions of monotone matrix equations, the convergence of linear asynchronous iteration with spectral radius of modulus one or aggregation and disaggregation methods for p-cyclic Markov chains are treated. On the other hand papers involved in optimization problems can be found. Nearly all fields of modern numerical analysis are touched by at least one paper.

Numerical Analysis

Numerical Analysis
Available:
Author: Anonim
Pages: 329
ISBN: 818750448X
Release: 2021
Editor: Academic Publishers

DESCRIPTION OF THE BOOK:

Introduction to Numerical Analysis

Introduction to Numerical Analysis
Available:
Author: J. Stoer,R. Bulirsch
Pages: 609
ISBN: 9781475755923
Release: 2013-04-17
Editor: Springer Science & Business Media

DESCRIPTION OF THE BOOK:

This book is based on a one-year introductory course on numerical analysis given by the authors at several universities in Germany and the United States. The authors concentrate on methods which can be worked out on a digital computer. For important topics, algorithmic descriptions (given more or less formally in ALGOL 60), as well as thorough but concise treatments of their theoretical founda tions, are provided. Where several methods for solving a problem are presented, comparisons of their applicability and limitations are offered. Each comparison is based on operation counts, theoretical properties such as convergence rates, and, more importantly, the intrinsic numerical properties that account for the reliability or unreliability of an algorithm. Within this context, the introductory chapter on error analysis plays a special role because it precisely describes basic concepts, such as the numerical stability of algorithms, that are indispensable in the thorough treatment of numerical questions. The remaining seven chapters are devoted to describing numerical methods in various contexts. In addition to covering standard topics, these chapters encom pass some special subjects not usually found in introductions to numerical analysis. Chapter 2, which discusses interpolation, gives an account of modem fast Fourier transform methods. In Chapter 3, extrapolation techniques for spe~d ing up the convergence of discretization methods in connection with Romberg integration are explained at length.

Numerical Analysis with Algorithms and Programming

Numerical Analysis with Algorithms and Programming
Available:
Author: Santanu Saha Ray
Pages: 708
ISBN: 9781315362212
Release: 2018-09-03
Editor: CRC Press

DESCRIPTION OF THE BOOK:

Numerical Analysis with Algorithms and Programming is the first comprehensive textbook to provide detailed coverage of numerical methods, their algorithms, and corresponding computer programs. It presents many techniques for the efficient numerical solution of problems in science and engineering. Along with numerous worked-out examples, end-of-chapter exercises, and Mathematica® programs, the book includes the standard algorithms for numerical computation: Root finding for nonlinear equations Interpolation and approximation of functions by simpler computational building blocks, such as polynomials and splines The solution of systems of linear equations and triangularization Approximation of functions and least square approximation Numerical differentiation and divided differences Numerical quadrature and integration Numerical solutions of ordinary differential equations (ODEs) and boundary value problems Numerical solution of partial differential equations (PDEs) The text develops students’ understanding of the construction of numerical algorithms and the applicability of the methods. By thoroughly studying the algorithms, students will discover how various methods provide accuracy, efficiency, scalability, and stability for large-scale systems.

Numerical Analysis for Engineers

Numerical Analysis for Engineers
Available:
Author: Bilal Ayyub,Richard H. McCuen
Pages: 456
ISBN: 1482250357
Release: 2015-10-02
Editor: Chapman and Hall/CRC

DESCRIPTION OF THE BOOK:

Designed for a one-semester undergraduate introduction to numerical methods, this text covers both the theory and practice of numerical methods for mathematics and engineering. With a wealth of exercises, it emphasizes the practical aspects of numerical methods and addresses their advantages and disadvantages. Novices and practicing engineers will understand the fundamentals, limitations, and potential of numerical methods.

Numerical Analysis

Numerical Analysis
Available:
Author: Walter Gautschi
Pages: 588
ISBN: 9780817682590
Release: 2011-12-07
Editor: Springer Science & Business Media

DESCRIPTION OF THE BOOK:

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.

A Brief Introduction to Numerical Analysis

A Brief Introduction to Numerical Analysis
Available:
Author: Eugene E. Tyrtyshnikov
Pages: 202
ISBN: 1461264138
Release: 2012-12-14
Editor: Birkhäuser

DESCRIPTION OF THE BOOK:

A logically organized advanced textbook, which turns the reader into an active participant by asking questions, hinting, giving direct recommendations, comparing different methods, and discussing "pessimistic" and "optimistic" approaches to numerical analysis. Advanced students and graduate students majoring in computer science, physics and mathematics will find this book helpful.

Schaum s Outline of Numerical Analysis

Schaum s Outline of Numerical Analysis
Available:
Author: Francis Scheid
Pages: 480
ISBN: 0070552215
Release: 1989-01-22
Editor: McGraw-Hill Education

DESCRIPTION OF THE BOOK:

If you want top grades and thorough understanding of numerical analysis, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you accompanying related problems with fully worked solutions. You also get additional problems to solve on your own, working at your own speed. (Answers at the back show you how you’re doing.) Famous for their clarity, wealth of illustrations and examples—and lack of dreary minutiae—Schaum’s Outlines have sold more than 30 million copies worldwide. This guide will show you why!

Dynamical Systems and Numerical Analysis

Dynamical Systems and Numerical Analysis
Available:
Author: Andrew Stuart,A. R. Humphries
Pages: 685
ISBN: 0521645638
Release: 1998-11-28
Editor: Cambridge University Press

DESCRIPTION OF THE BOOK:

This book unites the study of dynamical systems and numerical solution of differential equations. The first three chapters contain the elements of the theory of dynamical systems and the numerical solution of initial-value problems. In the remaining chapters, numerical methods are formulted as dynamical systems and the convergence and stability properties of the methods are examined. Topics studied include the stability of numerical methods for contractive, dissipative, gradient and Hamiltonian systems together with the convergence properties of equilibria, periodic solutions and strage attractors under numerical approximation. This book will be an invaluable tool for graduate students and researchers in the fields of numerical analysis and dynamical systems.