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matrix close to singular

From: Gerald Marewo
Subject: matrix close to singular
Date: Thu, 16 Nov 2000 17:24:15 +0200
User-agent: Mutt/1.2.5i

hi all.

i am working on a problem which involves the generalized eigenvalue

        given any two square matrices A and B, find matrices X and
        D that satisfy the following equation:

                A*X = B*X*D

        where D is a diagonal matrix of generalized eigenvalues and
        X is a matrix whose columns are the generalized

on the octave prompt if i type the following

        [X,D] = geig(A,B)

where geig.m is a user-defined function (below) that uses the qz

        function [V,D] = geig(A,B)
          [AA, BB, Q, Z, V, W, lambda] = qz (A, B);
          D = diag(lambda);

this should be equivalent to the matlab `eig' function.

for certain matrices i get the following warning:

 warning: inverse: matrix singular to machine precision, rcond =

in matlab i get a similar message:

 matrix is close to singular or badly scaled. results may be
 inaccurate. rcond = 5.678709e-018

is there a way of going round the problem of getting inaccurate
results. if there is a way of rescaling the matrix appropriately
please let me know?

any help will be greatly appreciated.

Gerald Marewo <address@hidden> using linux S.u.S.E;
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