FUNCTION: This is the ASCII overview file for the MATLAB codes accompanying the text Fundamentals of Numerical Computing. AUTHORS: Lawrence Shampine, Richard Allen, Steven Pruess DATE: January, 1998 These programs are implementations in MATLAB of the algorithms of the text. Because they are illustrative, they do not exploit fully the capabilities of the language. MATLAB is a computing environment that includes production-grade codes which in some cases are to be preferred. For instance, the \ operation is a polyalgorithm for the solution of linear systems that solves problems Factor and Solve do not address, viz. under- and over-determined systems. It recognizes automatically permutations of triangular matrices and symmetric positive definite matrices and deals with them appropriately. The computations are optimized for both language and hardware. Also, MATLAB 5 includes a new suite of ODE codes that are more powerful than Rke and Yvalue. The MATLAB versions of the programs have to be organized a little differently from other languages because prior to MATLAB 5, auxiliary functions had to be in separate files. All example programs state clearly which auxiliary functions are required to be in the path. Chapter 2 Systems of Linear Equations Tools... Factor.m: Factor decomposes the matrix A using Gaussian elimination and estimates its condition number. Factor is used in conjunction with Solve to solve A*x = b. Solve.m: Solve solves the linear system A*x = b using the decomposition obtained from Factor. Examples... Xlinsys.m: An example of the solution of a system of linear equations. REQUIRES Factor.m and Solve.m. Chapter 3 Interpolation Tools... Spcoef.m: Spcoef calculates coefficients defining a smooth cubic interpolatory spline S. Svalue.m: Evaluates the spline S at t using coefficients from Spcoef. Examples... Xspline.m: An example of interpolation with a complete cubic spline. REQUIRES Spcoef.m and Svalue.m. Chapter 4 Roots of Nonlinear Equations Tools... Zero.m: Zero computes a zero of the nonlinear equation f(x) = 0 when f(x) is a continuous real function of a single real variable x. Examples... Xzero.m: An example of finding a zero of a function. REQUIRES Zero.m and Xzerof.m. Xzerof.m: Function for Xzero.m. Chapter 5 Numerical Integration Tools... Adapt.m: Adapt estimates the definite integral of f(x) from a to b using an adaptive quadrature scheme based on Gauss-Kronrod (3,7) formulas. REQUIRES Add.m and Quad.m. Add.m: Auxiliary program required by Adapt. Adds an entry to the end of the queue. Quad.m: Auxiliary program required by Adapt. Does Gauss-Kronrod (3,7) quadrature over (alpha,beta). Examples... Xadapt.m: An example of computing a definite integral. REQUIRES Adapt.m, Add.m, Quad.m, and Xadaptf.m. Xadaptf.m: Function for Xadapt.m. Chapter 6 Initial Value Problems for Ordinary Differential Equations Tools... Rke.m: Rke integrates a system of neq first order ordinary differ- ential equations over one step using a Runge-Kutta method due to R. England. It provides for the evaluation of the solution within the step by interpolation. Yvalue.m: Evaluates quintic Hermite interpolants based on output from Rke. Examples... X1rke.m: An example of the solution of a system of ordinary differential equations using Rke. REQUIRES Rke.m and X1rkef.m. X1rkef.m: Function for example of X1rke.m. X2rke.m: An example of the solution of a system of ordinary differential equations using Rke and Yvalue. REQUIRES Rke.m, Yvalue.m, and X2rkef.m. X2rkef.m: Function for example of X2rke.m and of Xmrke.m. Xmrke.m: An example of the use of Rke that is more typical of computing in MATLAB. Same problem as in X2rke.m, but the solution is plotted both as a function of the independent variable and in the phase plane. REQUIRES Rke.m, Yvalue.m, and X2rkef.m. All these programs have been executed successfully using both MATLAB 4.2 and 5.1. Comments should be directed to shampine@na-net.ornl.gov.