TY  - JOUR
A1  - Eshghi, Nasim
A1  - Mach, Thomas
A1  - Reichel, Lothar
T1  - New matrix function approximations and quadrature rules based on the Arnoldi process
JF  - Journal of computational and applied mathematics
N2  - The Arnoldi process can be applied to inexpensively approximate matrix functions of the form f (A)v and matrix functionals of the form v*(f (A))*g(A)v, where A is a large square non-Hermitian matrix, v is a vector, and the superscript * denotes transposition and complex conjugation. Here f and g are analytic functions that are defined in suitable regions in the complex plane. This paper reviews available approximation methods and describes new ones that provide higher accuracy for essentially the same computational effort by exploiting available, but generally not used, moment information. Numerical experiments show that in some cases the modifications of the Arnoldi decompositions proposed can improve the accuracy of v*(f (A))*g(A)v about as much as performing an additional step of the Arnoldi process.
KW  - Arnoldi process
KW  - Matrix function approximation
KW  - Quadrature rule
Y1  - 2021
U6  - https://doi.org/10.1016/j.cam.2021.113442
SN  - 0377-0427
SN  - 1879-1778
VL  - 391
PB  - Elsevier
CY  - Amsterdam
ER  -