Analysis of some Krylov subspace approximations to the matrix exponential operator
SIAM Journal on Numerical Analysis
Approximation of matrix-valued functions
SIAM Journal on Matrix Analysis and Applications
Rational approximations from power series of vector-valued meromorphic functions
Journal of Approximation Theory
On Krylov Subspace Approximations to the Matrix Exponential Operator
SIAM Journal on Numerical Analysis
Multivariate generalized inverse vector-valued rational interpolants
Journal of Computational and Applied Mathematics
Vector valued Thiele-Werner-type osculatory rational interpolants
Journal of Computational and Applied Mathematics - Special issue on proceedings of the international symposium on computational mathematics and applications
The Scaling and Squaring Method for the Matrix Exponential Revisited
SIAM Journal on Matrix Analysis and Applications
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Functions of Matrices: Theory and Computation (Other Titles in Applied Mathematics)
Computing $A^\alpha, \log(A)$, and Related Matrix Functions by Contour Integrals
SIAM Journal on Numerical Analysis
A New Scaling and Squaring Algorithm for the Matrix Exponential
SIAM Journal on Matrix Analysis and Applications
| Hi-index | 7.29 |
In this paper a new method for computing the action of the matrix exponential on a vector e^A^tb, where A is a complex matrix and t is a positive real number, is proposed. Our approach is based on vector valued rational approximation where the approximants are determined by the denominator polynomials whose coefficients are obtained by solving an inexpensive linear least-squares problem. No matrix multiplications or divisions but matrix-vector products are required in the whole process. A technique of scaling and recurrence enables our method to be more effective when the problem is for fixed A,b and many values of t. We also give a backward error analysis in exact arithmetic for the truncation errors to derive our new algorithm. Preliminary numerical results illustrate that the new algorithm performs well.