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Introduction to Numerical Analysis

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Hardcover | 26 September 2001

At a Glance

Hardcover
366 Pages

Dimensions(cm)
22.86 x 15.24 x 2.39

Hardcover

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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.

Industry Reviews

'... 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

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You Can Find This Book In

Non-Fiction Mathematics Applied Mathematics Probability & Statistics Calculus & Mathematical Analysis Numerical Analysis Number Theory

Preface	p. vii
The Numerical Evaluation of Expressions	p. 1
Arithmetic Expressions and Automatic Differentiation	p. 2
Numbers, Operations, and Elementary Functions	p. 14
Numerical Stability	p. 23
Error Propagation and Condition	p. 33
Interval Arithmetic	p. 38
Exercises	p. 53
Linear Systems of Equations	p. 61
Gaussian Elimination	p. 63
Variations on a Theme	p. 73
Rounding Errors, Equilibration, and Pivot Search	p. 82
Vector and Matrix Norms	p. 94
Condition Numbers and Data Perturbations	p. 99
Iterative Refinement	p. 106
Error Bounds for Solutions of Linear Systems	p. 112
Exercises	p. 119
Interpolation and Numerical Differentiation	p. 130
Interpolation by Polynomials	p. 131
Extrapolation and Numerical Differentiation	p. 145
Cubic Splines	p. 153
Approximation by Splines	p. 165
Radial Basis Functions	p. 170
Exercises	p. 182
Numerical Integration	p. 179
The Accuracy of Quadrature Formulas	p. 179
Gaussian Quadrature Formulas	p. 187
The Trapezoidal Rule	p. 196
Adaptive Integration	p. 203
Solving Ordinary Differential Equations	p. 210
Step Size and Order Control	p. 219
Exercises	p. 225
Univariate Nonlinear Equations	p. 233
The Secant Method	p. 234
Bisection Methods	p. 241
Spectral Bisection Methods for Eigenvalues	p. 250
Convergence Order	p. 256
Error Analysis	p. 265
Complex Zeros	p. 273
Methods Using Derivative Information	p. 281
Exercises	p. 293
Systems of Nonlinear Equations	p. 301
Preliminaries	p. 302
Newton's Method and Its Variants	p. 311
Error Analysis	p. 322
Further Techniques for Nonlinear Systems	p. 329
Exercises	p. 340
References	p. 345
Index	p. 351
Table of Contents provided by Syndetics. All Rights Reserved.

Introduction to Numerical Analysis

At a Glance

Hardcover

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