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A new algorithm for the computation of the smallest eigenvalue of
a symmetric matrix and its eigenspace

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B. Jansen, C. Roos, T. Terlaky

The problem of finding the smallest eigenvalue and the corresponding
eigenspace of a symmetric matrix
is stated as a semidefinite optimization problem.
A straightforward application of nowadays more or less standard routines
for the solution of semidefinite problems yields a new algorithm for
the smallest eigenvalue problem; the approach not only yields the smallest
eigenvalue, but also a symmetric positive semidefinite (SPSD)
matrix whose column space is equal to the eigenspace for the
smallest eigenvalue. It is shown that the predictor-corrector method
yields a polynomial time algorithm which,
with a suitable choice of the step size,
asymptotically is quadratically convergent.

Report 95-70, Faculty of Technical Mathematics and Computer Science,
Delft University of Technology, Delft, 1995.

Contact: t.terlaky@twi.tudelft.nl