On Krylov Subspace Approximations to the Matrix Exponential Operator

On Krylov Subspace Approximations to Thematrix Exponential

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...

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...

A nested Krylov subspace method for the overlap operator

We present a novel method to compute the overlap Dirac operator at zero and nonzero quark chemical potential. To approximate the sign function of large, sparse matrices, standard methods project the operator on a much smaller Krylov subspace, on which the matrix function is computed exactly. However, for large lattices this subspace can still be too large for an efficient calculation of the sig...

Inexact Krylov Subspace Algorithms for Large Matrix Exponential Eigenproblem from Dimensionality Reduction

Matrix exponential discriminant analysis (EDA) is a generalized discriminant analysis method based on matrix exponential. It can essentially overcome the intrinsic difficulty of small sample size problem that exists in the classical linear discriminant analysis (LDA). However, for data with high dimension, one has to solve a large matrix exponential eigenproblem in this method, and the time com...