We examined the two proposed methods with a number of random linear interval systems [mathematical expression not reproducible] when [??] [member of] [IR.sup.nxn] is a random interval symmetric

diagonally dominant matrix. Tables 4 and 5 show the number of iterations needed by our presented methods to find the solution with tolerances [theta] = [10.sup.-3] and [theta] = [10.sup.-7] for random interval systems with various dimensions.

Hence, [G.sup.N.sub.[beta],k] is a strongly

diagonally dominant matrix.

We know that A is called a strictly

diagonally dominant matrix if

Note moreover, that for small values of the parameters, we obtain a

diagonally dominant matrix. Hence, the rank of each class will depend mostly on the values within the class but the problem will become close to reducibility and therefore numerically unstable.

In Figure 6.1, the upper left matrix is the original block

diagonally dominant matrix, where we clearly can distinguish the diagonal blocks.

For the second example we use a banded

diagonally dominant matrix with sixteen nonzero diagonals.

ALAN GEORGE AND KHAKIM IKRAMOV, Gaussian Elimination for the Inverse of a

Diagonally Dominant Matrix is Stable, Math.

Let A be a normalized symmetric positive definite

diagonally dominant matrix, and let [alpha]E, [alpha] [member of] [C.sup.+] = {z [member of] C : Re(z) [greater than or equal to] 0}, be a diagonal matrix whose entries have positive real part.

Given any matrix A = [[a.sub.i,i]] [member of] [C.sup.n x 2], and given any nonempty subset S of N, then A is an S-strictly

diagonally dominant matrix if