- Backward rounding error in the
Choleski decomposition (Mar 18 2009)
% This example illustrates the fact that the standard backward
% rounding-error bound for the Cholesky decomposition can be much larger
% than the backward error itself. It generates a symmetric positive
% definite matrix of order n with norm 1 and condition number 10^t. It
% then computes the Cholesky factor R in single precision and the
% backward error A - R'*R in double precision. The classical bound is
% printed out for comparison (see Higham, Accuracy and Stability of
% Numerical Algorithms, 2nd edition, p. 198).
- Convergence of a divergent sum (Mar 18 2009)
% This script can be used to explain how a divergent sum can converge in
% finite precision arithmetic--in this case in 2-digit decimal
% floating-point arithmetic. In the first run, the sum becomes
% stationary when it reaches a value of 3.9. The second run prints out
% enough additional information to show what is going on. The teacher
% can supply running comments.
- Rounding error and the quadratic formula
(Mar 18 2009)
% This example solves a quadratic equation using the standard quadratic
% formula. The smallest root is completely inaccurate. A cure is
% illustrated. The script produces comments as it proceeds.
- Properties of iterative refinement (Mar 18 2009)
% This script generates a a matrix A of order 100 with condition number
% 10^sig. It also generates the right hand side of a linear system Ax=b
% and an approximate solution xt that is accurate to about 16-sig
% decimal digits. The linear system is then solved with an underlying
% precision of rho decimal digits and performs four steps of iterative
% refiniment with the residual evaluated in tau-digit decimal floating
% point arithmetic.