# diagonally dominant matrix

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## diagonally dominant matrix

[dī′ag·ən·əl·ē ′däm·ə·nənt ′mā‚triks]
(mathematics)
A matrix in which the absolute value of each diagonal element is either greater than the sum of the absolute values of the off-diagonal elements of the same row or greater than the sum of the off-diagonal elements in the same column.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
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
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