Numerical Methods, Software and Analysis

Abstract

2nd ed. 1. Mathematics and Computer Science Background -- 1.1. Calculus -- 1.2. Vectors, Matrices, and Linear Equations -- 1.3. Differential Equations -- 1.4. Programming -- 2. Numerical Software -- 2.1. Library Concept -- 2.2. Using a Library -- 2.3. Standard Numerical Software -- 2.4. IMSL Mathematics Library -- 2.5. PROTRAN System -- 3. Errors, Round-Off, and Stability -- 3.1. Sources of Uncertainty -- 3.2. Numerical Approximations -- 3.3. Round-Off Errors -- 3.4. Case Study: Calculation of [pi] -- 3.5. How to Estimate Errors and Uncertainty -- 4. Models and Formulas for Numerical Computation -- 4.1. Polynomials -- 4.2. Piecewise Polynomials -- 4.3. Splines -- 4.4. Other Piecewise Polynomials and Splines with Multiple Knots -- 4.5. General Methods for Deriving Formulas -- 5. Interpolation -- 5.1. General Interpolation Using Linear Equation Solvers -- 5.2. Interpolation Methods for Polynomials -- 5.3. Interpolation Methods for Piecewise Polynomials -- 5.4. Software for Interpolation -- 5.5. Choice of Interpolation Forms and Points -- 5.6. Error Analysis for Interpolation -- 6. Matrices and Linear Equations -- 6.1. Types and Sources of Matrix Computation Problems -- 6.2. Gauss Elimination, Lu-Factorization, and Pivoting -- 6.3. Iteration Methods for Linear Systems -- 6.4. Software for Linear Equations -- 6.5. Case Study: Design of the Interface for a Linear Equations Solver -- 6.6. Analysis of the Linear Equations Problem -- 6.7. Eigensystem Problems and Software -- 7. Differentiation and Integration -- 7.1. Methods for Estimating Derivatives -- 7.2. Software for Differentiation -- 7.3. Error Analysis for Differentiation -- 7.4. Estimation of Integrals -- 7.5. Adaptive Quadrature -- 7.6. Software for Integration -- 7.7.