Bounds for the Trace of the Inverse and the Determinantof Symmetric Positive De nite
نویسنده
چکیده
Dedicated to T. Rivlin on the occasion of his 70th birthday Lower and upper bounds are given for the trace of the inverse tr(A ?1) and the determinant det(A) of a symmetric positive deenite matrix A. They are derived by applying Gaussian quadrature and related theory. The bounds for det(A) appears to be new. For the bounds of tr(A ?1), the Kantorovich inequality is available for providing such bounds. In a number of examples, our bounds are found to be tighter when simple trial vectors are used in Kantorovich's bound. The new bounds are equivalent to Robinson and Wathen's variational bounds. But our bounds are directly derived for the quantity instead of the summation of bounds for each diagonal entry of A ?1 .
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