Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator

Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator

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 matr...

On Krylov Subspace Approximations to Thematrix Exponential

extensions of some polynomial inequalities to the polar derivative

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Preconditioning Lanczos Approximations to the Matrix Exponential

The Lanczos method is an iterative procedure to compute an orthogonal basis for the Krylov subspace generated by a symmetric matrix A and a starting vector v. An interesting application of this method is the computation of the matrix exponential exp(−τA)v. This vector plays an important role in the solution of parabolic equations where A results from some form of discretization of an elliptic o...

Convergence Analysis of an Extended Krylov Subspace Method for the Approximation of Operator Functions in Exponential Integrators

We analyze the convergence of an extended Krylov subspace method for the approximation of operator functions that appear in exponential integrators. For operators, the size of the polynomial part of the extended Krylov subspace is restricted according to the smoothness of the initial data. This restriction for the continuous operator has a significant influence on the approximation of matrix fu...