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Annotation of researchv10dc/cmd/matlab/demo, revision 1.1

1.1     ! root        1: //Eigenvalue sensitivity example. See section 8 of the Users' Guide.
        !             2: B = <3 0 7; 0 2 0; 0 0 1>
        !             3: L = <1 0 0; 2 1 0; -3 4 1>,  M = L\L'
        !             4: A = M*B/M
        !             5: A = round(A)
        !             6: <X,D> = eig(A)
        !             7: long,  diag(D),  short
        !             8: cond(X)
        !             9: X = X/diag(X(3,:)),  cond(X)
        !            10: Y = inv(X'),  Y'*A*X
        !            11: for j = 1:3, c(j) = norm(Y(:,j))*norm(X(:,j));
        !            12: C
        !            13: E = -1.e-6*Y(:,1)*X(:,1)'
        !            14: eig(A + .4*E),  eig(A + .5*E)
        !            15: r = .4;  s = .5;
        !            16: while s-r > 1.e-14, t = (r+s)/2; d = eig(A+t*E); ...
        !            17:   if imag(d(1))=0, r = t; else, s = t;
        !            18: long,  t = r
        !            19: A+t*e,  eig(A+t*E)
        !            20: <X,D> = eig(A+t*E);  X = X/diag(X(3,:))
        !            21: short,  cond(X)

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