Shift-invert Rational Krylov method for an operator phi-function of an unbounded linear operator

摘要

The product of a matrix function and a vector is used to solve evolution equations numerically. Hashimoto and Nodera(ANZIAM J 58:C149-C161, 2016) proposed the Shift-invert Rational Krylov method for computing these products. However, since matrices produced by evolution equations behave like unbounded operators in infinite-dimensional spaces, an analysis with the unbounded operator is essential. In this paper, the Shift-invert Rational Krylov method is extended to be applied to unbounded operators.