Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator Export

@article{citeulike:3440962, abstract = {In this note a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation exp(A)v is presented, and a priori and a posteriori error estimates are established. Several such approximations are considered. The main idea of these techniques is to approximately project the exponential operator onto a small Krylov subspace and to 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.}, author = {Saad, Y.}, citeulike-article-id = {3440962}, citeulike-linkout-0 = {http://dx.doi.org/10.2307/2158085}, citeulike-linkout-1 = {http://www.jstor.org/stable/2158085}, doi = {10.2307/2158085}, issn = {00361429}, journal = {SIAM Journal on Numerical Analysis}, keywords = {exponential, matrix}, number = {1}, pages = {209--228}, posted-at = {2008-10-22 18:27:29}, priority = {2}, publisher = {Society for Industrial and Applied Mathematics}, title = {Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator}, url = {http://dx.doi.org/10.2307/2158085}, volume = {29}, year = {1992} }

TY - JOUR ID - citeulike:3440962 L3 - citeulike-article-id:3440962 N2 - In this note a theoretical analysis of some Krylov subspace approximations to the matrix exponential operation exp(A)v is presented, and a priori and a posteriori error estimates are established. Several such approximations are considered. The main idea of these techniques is to approximately project the exponential operator onto a small Krylov subspace and to 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. IS - 1 JF - SIAM Journal on Numerical Analysis SN - 00361429 EP - 228 TI - Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator PB - Society for Industrial and Applied Mathematics VL - 29 SP - 209 KW - exponential KW - matrix AU - Saad, Y PY - 1992/// UR - http://dx.doi.org/10.2307/2158085 ER -