Shift-invert rational Krylov method for evolution equations

Yuka Hashimoto, Takashi Nodera


In order to obtain the numerical solution of evolution equations which arise in various fields of science and technology, the computation of matrix functions called \(\phi\)-functions is required. This paper proposes a new method called the shift-invert rational Krylov method for the computation of matrix \(\phi\)-functions. This method efficiently computes the matrix \(\phi\)-functions and allows the appropriate parameters to be simply determined.

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Shift-invert rational Krylov, $\phi$-function

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