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9780521336109

Introduction to Numerical Analysis

by
  • ISBN13:

    9780521336109

  • ISBN10:

    0521336104

  • Format: Paperback
  • Copyright: 2001-10-01
  • Publisher: Cambridge University Press

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Summary

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.

Author Biography

Arnold Neumaier is a Professor of Computational Mathematics at the University of Wien

Table of Contents

Preface vii
The Numerical Evaluation of Expressions
1(60)
Arithmetic Expressions and Automatic Differentiation
2(12)
Numbers, Operations, and Elementary Functions
14(9)
Numerical Stability
23(10)
Error Propagation and Condition
33(5)
Interval Arithmetic
38(15)
Exercises
53(8)
Linear Systems of Equations
61(69)
Gaussian Elimination
63(10)
Variations on a Theme
73(9)
Rounding Errors, Equilibration, and Pivot Search
82(12)
Vector and Matrix Norms
94(5)
Condition Numbers and Data Perturbations
99(7)
Iterative Refinement
106(6)
Error Bounds for Solutions of Linear Systems
112(7)
Exercises
119(11)
Interpolation and Numerical Differentiation
130(49)
Interpolation by Polynomials
131(14)
Extrapolation and Numerical Differentiation
145(8)
Cubic Splines
153(12)
Approximation by Splines
165(5)
Radial Basis Functions
170(12)
Exercises
182
Numerical Integration
179(54)
The Accuracy of Quadrature Formulas
179(8)
Gaussian Quadrature Formulas
187(9)
The Trapezoidal Rule
196(7)
Adaptive Integration
203(7)
Solving Ordinary Differential Equations
210(9)
Step Size and Order Control
219(6)
Exercises
225(8)
Univariate Nonlinear Equations
233(68)
The Secant Method
234(7)
Bisection Methods
241(9)
Spectral Bisection Methods for Eigenvalues
250(6)
Convergence Order
256(9)
Error Analysis
265(8)
Complex Zeros
273(8)
Methods Using Derivative Information
281(12)
Exercises
293(8)
Systems of Nonlinear Equations
301(44)
Preliminaries
302(9)
Newton's Method and Its Variants
311(11)
Error Analysis
322(7)
Further Techniques for Nonlinear Systems
329(11)
Exercises
340(5)
References 345(6)
Index 351

Supplemental Materials

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The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

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