Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator
نویسنده
چکیده
In this note we present a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation exp(A)v and establish a priori and a posteriori error estimates. Several such approximations are considered. The main idea of these techniques is to approximately project the exponential operator onto a small Krylov subspace and carry out the resulting small exponential matrix computation accurately. This general approach, which has been used with success in several applications, provides a systematic way of defining high order explicit-type schemes for solving systems of ordinary differential equations or time-dependent Partial Differential Equations.
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