on the occasion of this new edition, the text was enlarged by several new sections. two sections on b-splines and their computation were added to the chapter on spline functions: due to their special properties, their flexibility, and the availability of well-tested programs for their computation, b-splines play an important role in many applications. also, the authors followed suggestions by many readers to supplement the chapter on elimination methods with a section dealing with the solution of large sparse systems of linear equations. even though such systems are usually solved by iterative methods, the realm of elimination methods has been widely extended due to powerful techniques for handling sparse matrices. we will explain some of these techniques in connection with the cholesky algorithm for solving positive definite linear systems.
目录
Preface to the Second Edition Preface to the First Edition 1 Error Analysis 1.1 Representation of Numbers 1.2 Roundoff Errors and Floating-Point Arithmetic 1.3 Error Propagation 1.4 Examples 1.5 Interval Arithmetic； Statistical Roundoff Estimation Exercises for Chapter 1 References for Chapter 1 2 Interpolation 2.1 Interpolation by Polynomials 2.1.1 Theoretical Foundation: The Interpolation Formula of Lagrange 2.1.2 Neville‘s Algorithm 2.1.3 Newton‘s Interpolation Formula: Divided Differences 2.1.4 The Error in Polynomial Interpolation 2.1.5 Hermite Interpolation 2.2 Interpolation by Rational Functions 2.2.1 General Properties of Rational Interpolation 2.2.2 Inverse and Reciprocal Differences. Thiele‘s Continued Fraction 2.2.3 Algorithms of the Neville Type 2.2.4 Comparing Rational and Polynomial Interpolations 2.3 Trigonometric Interpolation …… 3 Topics in Integration 4 Systems of Linear Equations 5 Finding Zeros nad Minim by Iterative Methods 6 Eigenvalue Problems 7 Ordinary Differential Equations 8 Iterative Methods for the Solution of Large Systems of Linear Equation.Some Further Methods General Literature on Numerical Methods Index
