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Introduction to Numerical Analysis - Arnold Neumaier

Introduction to Numerical Analysis

Hardcover

Published: 23rd January 2015
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Numerical analysis is an increasingly important link between pure mathematics and its application in science and technology. This textbook provides an introduction to the justification and development of constructive methods that provide sufficiently accurate approximations to the solution of numerical problems, and the analysis of the influence that errors in data, finite-precision calculations, and approximation formulas have on results, problem formulation and the choice of method. It also serves as an introduction to scientific programming in MATLAB, including many simple and difficult, theoretical and computational exercises. A unique feature of this book is the consequent development of interval analysis as a tool for rigorous computation and computer assisted proofs, along with the traditional material.

'... very valuable in preparing a course on Numerical Analysis and is indeed very readable.' Thomas Sonar, Zentralblatt MATH 'This is very strongly recommended reading for all undergraduate students whose courses require a serious understanding and implementation of numerical analysis.' The Mathematical Gazette

Prefacep. vii
The Numerical Evaluation of Expressionsp. 1
Arithmetic Expressions and Automatic Differentiationp. 2
Numbers, Operations, and Elementary Functionsp. 14
Numerical Stabilityp. 23
Error Propagation and Conditionp. 33
Interval Arithmeticp. 38
Exercisesp. 53
Linear Systems of Equationsp. 61
Gaussian Eliminationp. 63
Variations on a Themep. 73
Rounding Errors, Equilibration, and Pivot Searchp. 82
Vector and Matrix Normsp. 94
Condition Numbers and Data Perturbationsp. 99
Iterative Refinementp. 106
Error Bounds for Solutions of Linear Systemsp. 112
Exercisesp. 119
Interpolation and Numerical Differentiationp. 130
Interpolation by Polynomialsp. 131
Extrapolation and Numerical Differentiationp. 145
Cubic Splinesp. 153
Approximation by Splinesp. 165
Radial Basis Functionsp. 170
Exercisesp. 182
Numerical Integrationp. 179
The Accuracy of Quadrature Formulasp. 179
Gaussian Quadrature Formulasp. 187
The Trapezoidal Rulep. 196
Adaptive Integrationp. 203
Solving Ordinary Differential Equationsp. 210
Step Size and Order Controlp. 219
Exercisesp. 225
Univariate Nonlinear Equationsp. 233
The Secant Methodp. 234
Bisection Methodsp. 241
Spectral Bisection Methods for Eigenvaluesp. 250
Convergence Orderp. 256
Error Analysisp. 265
Complex Zerosp. 273
Methods Using Derivative Informationp. 281
Exercisesp. 293
Systems of Nonlinear Equationsp. 301
Preliminariesp. 302
Newton's Method and Its Variantsp. 311
Error Analysisp. 322
Further Techniques for Nonlinear Systemsp. 329
Exercisesp. 340
Referencesp. 345
Indexp. 351
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780521333238
ISBN-10: 0521333237
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 366
Published: 23rd January 2015
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.4
Weight (kg): 0.71