Introduction to numerical analysis

Includes Index

Cover; Title Page; Copyright Page; Contents; Preface; 1.1 Numerical Analysis; 1.2 Approximation; 1.3 Errors; 1.4 Significant Figures; 1.5 Determinacy of Functions. Error Control; 1.6 Machine Errors; 1.7 Random Errors; 1.8 Recursive Computation; 1.9 Mathematical Preliminaries; 1.10 Supplementary References; Problems; 1 Introduction; 2 Interpolation with Divided Differences; 2.1 Introduction; 2.2 Linear Interpolation; 2.3 Divided Differences; 2.4 Second-Degree Interpolation; 2.5 Newton's Fundamental Formula; 2.6 Error Formulas; 2.7 Iterated Interpolation; 2.8 Inverse Interpolation. 2.9 Supplementary ReferencesProblems; 3 Lagrangian Methods; 3.1 Introduction; 3.2 Lagrange's Interpolation Formula; 3.3 Numerical Differentiation and Integration; 3.4 Uniform-spacing Interpolation; 3.5 Newton-Cotes Integration Formulas; 3.6 Composite Integration Formulas; 3.7 Use of Integration Formulas; 3.8 Richardson Extrapolation. Romberg Integration; 3.9 Asymptotic Behavior of Newton-Cotes Formulas; 3.10 Weighting Functions. Filon Integration; 3.11 Differentiation Formulas; 3.12 Supplementary References; Problems; 4 Finite-Difference Interpolation; 4.1 Introduction. 4.2 Difference Notations4.3 Newton Forward- and Backward-difference Formulas; 4.4 Gaussian Formulas; 4.5 Stirling's Formula; 4.6 Bessel's Formula; 4.7 Everett's Formulas; 4.8 Use of Interpolation Formulas; 4.9 Propagation of Inherent Errors; 4.10 Throwback Techniques; 4.11 Interpolation Series; 4.12 Tables of Interpolation Coefficients; 4.13 Supplementary References; Problems; 5 Operations with Finite Differences; 5.1 Introduction; 5.2 Difference Operators; 5.3 Differentiation Formulas; 5.4 Newtonian Integration Formulas; 5.5 Newtonian Formulas for Repeated Integration. 5.6 Central-Difference Integration Formulas5.7 Subtabulation; 5.8 Summation and Integration. The Euler-Maclaurin Sum Formula; 5.9 Approximate Summation; 5.10 Error Terms in Integration Formulas; 5.11 Other Representations of Error Terms; 5.12 Supplementary References; Problems; 6 Numerical Solution of Differential Equations; 6.1 Introduction; 6.2 Formulas of Open Type; 6.3 Formulas of Closed Type; 6.4 Start of Solution; 6.5 Methods Based on Open-Type Formulas; 6.6 Methods Based on Closed-Type Formulas. Prediction-Correction Methods; 6.7 The Special Case F = Ay; 6.8 Propagated-Error Bounds. 6.9 Application to Equations of Higher Order. Sets of Equations6.10 Special Second-order Equations; 6.11 Change of Interval; 6.12 Use of Higher Derivatives; 6.13 A Simple Runge-Kutta Method; 6.14 Runge-Kutta Methods of Higher Order; 6.15 Boundary-Value Problems; 6.16 Linear Characteristic-value Problems; 6.17 Selection of a Method; 6.18 Supplementary References; Problems; 7 Least-Squares Polynomial Approximation; 7.1 Introduction; 7.2 The Principle of Least Squares; 7.3 Least-Squares Approximation over Discrete Sets of Points; 7.4 Error Estimation; 7.5 Orthogonal Polynomials.

Well-known, respected introduction, updated to integrate concepts and procedures associated with computers. Computation, approximation, interpolation, numerical differentiation and integration, smoothing of data, other topics in lucid presentation. Includes 150 additional problems in this edition. Bibliography.