# Chapter 10, Computer Assisted Proofs and Self-Validating Methods

### Siegfried M. Rump

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

Last modified: January 23, 2006