FUNDAMENTALS OF NUMERICAL COMPUTING
CONTENTS CHAPTER ERRORS AND FLOATING POINT ARITHMETIC 1 1 BASIC CONCEPTS EXAMPLES OF FLOATING POINT CALCULATIONS CASE STUDY 1 FURTHER READING CHAPTER SYSTEMS OF LINEAR EQUATIONS 2 1 GAUSSIAN ELIMINATION WITH PARTIAL PIVOTING 2 2 MATRIX FACTORIZATION 2 3 ACCURACY 2 4 ROUTINES FACTOR AND SOLVE 2 5 MATRICES WITH SPECIAL STRUCTURE 2 6 CASE STUDY 2 INTERPOLATION 3 1 POLYNOMIAL INTERPOLATION 3 2 MORE ERROR BOUNDS 3 3 NEWTON DIVIDED DIFFERENCE FORM 3 4 ASSESSING ACCURACY 3 5 SPLINE INTERPOLATION 3 6 INTERPOLATION IN THE PLANE 3 7 CASE STUDY 3 ROOTS OF NONLINEAR EQUATIONS BISECTION, NEWTON’S METHOD, AND THE SECANT RULE AN ALGORITHM COMBINING BISECTION AND THE SECANT RULE ROUTINES FOR ZERO FINDING CONDITION, LIMITING PRECISION, AND MULTIPLE ROOTS 4 5 NONLINEAR SYSTEMS OF EQUATIONS 4 6 CASE STUDY 4 NUMERICAL INTEGRATION 5 1 BASIC QUADRATURE RULES 5 2 ADAPTIVE QUADRATURE 5 3 CODES FOR ADAPTIVE QUADRATURE 5 4 SPECIAL DEVICES FOR INTEGRATION 5 5 INTEGRATION OF TABULAR DATA 5 6 INTEGRATION IN TWO VARIABLES 5 7 CASE STUDY 5 ORDINARY DIFFERENTIAL EQUATIONS 6 1 SOME ELEMENTS OF THE THEORY 6 2 A SIMPLE NUMERICAL SCHEME 6 3 ONE-STEP METHODS 6 4 ERRORS-LOCAL AND GLOBAL 6 5 THE ALGORITHMS 6 6 THE CODE RKE 6 7 OTHER NUMERICAL METHODS 6 8 CASE STUDY 6