Double-shift-invert Arnoldi method for computing the matrix exponential

Computing the matrix exponential for large sparse matrices is essential for solving evolution equations numerically. Conventionally, the shift-invert Arnoldi method is used to compute a matrix exponential and a vector product. This method transforms the original matrix using a shift, and generates the Krylov subspace of the transformed matrix for approximation. The transformation makes the approximation converge faster. In this paper, a new method called the double-shift-invert Arnoldi method is explored. This method uses two shifts for transforming the matrix, and this transformation results in a faster convergence than the shift-invert Arnoldi method.