Numerical evaluation of operator determinants

Issa Karambal

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arXiv · 1210.4076

Numerical evaluation of operator determinants

Issa Karambal

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Abstract

For any integral operator $K$ in the Schatten--von Neumann classes of compact operators and its approximated operator $K_N\sim(N\ge1)$ obtained by using for example a quadrature or projection method, we show that the convergence of the approximate $p$-modified Fredholm determinants $\sideset{}{_{Np}}\det(I_N+zK_N)$ to the $p$-modified Fredholm determinants $\sideset{}{_p}\det(I_\mathcal{H}+zK)$ is uniform for all $p\ge1$. As a result, we give the rate of convergences when evaluating at an eigenvalue or at an element of the resolvent set of $K$.

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Issa Karambal. 2012-10-15. Numerical evaluation of operator determinants. https://arxiv.org/abs/1210.4076

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