Chapter 10, Computer Assisted Proofs and Self-Validating Methods

In this chapter both graphic illustrations and program excerpts are numbered as figures.

• Figure 10.1 IBM Prime Letterhead
• Figure 10.2 University of Illinois Postmark
• Figure 10.3 Pocket calculators with 8 decimal digits, no exponent
• Figure 10.4 Point matrix times interval vector
• Figure 10.7 Naive interval Gaussian elimination: growth of rad(U_ii)
• Figure 10.8 Plot of the function in equation (10.8) with 20 meshpoints in x- and y-directions
• Figure 10.9 Plot of the function in equation (10.8) with 50 meshpoints in x- and y-directions
• Figure 10.11 Comparison of a naive algorithm and a self-validating method
• Figure 10.23 Inclusion as computed by verifylss for the example in Table 10.12
• Figure 10.24 Inner and outer inclusion and true solution set for the example in Table 10.12
• Figure 10.26 Result of Monte Carlo approach for the example in Table 10.12
• Figure 10.27 Inner and outer inclusion and true solution set for the example in Table 10.12
• Figure 10.28 Nonzero elements of the matrix from Harwell/Boeing BCSSTK15
• Figure 10.29 Approximation of eigenvalues of the matrix in Table 10.14 computed by MATLAB