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dispmat_gersh

Draw the Gershgorin circles of the matrix.

Calling Sequence

h = dispmat_gersh ( A )

Parameters

A :

a nxn matrix of doubles

h :

graphics handle

Description

Plots the Gershgorin circles of the matrix. We assume that A is a n-by-n square matrix. The matrix may be either real or complex. Hence, there are n circles. Each circle i=1,2,...,n has center (x_i,y_i), where x_i and y_i are the real and imaginary parts of the diagonal element A(i,i). The radius of each circle is the sum of the absolute value of the off-diagonal entries in the row i. This can be computed with the vectorized statement:

r(i) = sum(abs(A(i,:))) - abs(A(i,i))

The Gershgoring circle theorem states that every eigenvalue of A lies within at least one of the Gershgorin discs. If the union #1 of k discs is disjoint from the union #2 of the other n ? k discs then the union #1 contains exactly k and the union #2 contains exactly n ? k eigenvalues of A.

Examples

A = [
10 -1 0 1
0.2 8 0.2 0.2
1 1 2 1
-1 -1 -1 -11
];
dispmat_gersh(A)
spec(A)

Authors

Bibliography

http://en.wikipedia.org/wiki/Gershgorin_circle_theorem


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