ART: Adaptive residual-time restarting for Krylov subspace matrix exponential evaluations

Residual, Restarting, and Richardson Iteration for the Matrix Exponential

Abstract. A well-known problem in computing some matrix functions iteratively is a lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Assume, the matrix exponential of a given matrix times a given vector has to be computed. We interpret the sought after vector as a value of a vector function satisfying the linea...

Residual, restarting and Richardson iteration for the matrix exponential, revised

Abstract. A well-known problem in computing some matrix functions iteratively is the lack of a clear, commonly accepted residual notion. An important matrix function for which this is the case is the matrix exponential. Suppose the matrix exponential of a given matrix times a given vector has to be computed. We develop the approach of Druskin, Greenbaum and Knizhnerman (1998) and interpret the ...

On Krylov Subspace Approximations to Thematrix Exponential

A new investigation of the extended Krylov subspace method for matrix function evaluations

For large square matrices A and functions f , the numerical approximation of the action of f(A) to a vector v has received considerable attention in the last two decades. In this paper we investigate the Extended Krylov subspace method, a technique that was recently proposed to approximate f(A)v for A symmetric. We provide a new theoretical analysis of the method, which improves the original re...

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...