Shift-invert Rational Krylov method for an operator \(\phi \)-function of an unbounded linear operator
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.
KeywordsKrylov subspace method Operator function Unbounded operator \(\phi \)-function
Mathematics Subject Classification65F60 65M22 47A60
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