Fetching the paper…
Reading the bibliography…
In this paper, we present new a posteriori and a priori error bounds for the Krylov subspace methods for computing $e^{-\tau A}v$ for a given $\tau>0$ and $v \in C^n$, where $A$ is a large sparse non-Hermitian matrix.
M. Hochbruck and C. Lubich, On Krylov subspace approximations to the matrix exponential operator , SIAM J. Numer. Anal., 34 (1997), pp. 1911-1925
1925
Earlier work this paper cites.
L. M. Milne-Thomson, Jacobian Elliptic Function Tables , Dover Publications INC., 1950
1950
Earlier work this paper cites.
H. Kober, Dictionary of Conformal Representations , Dover Publications INC., 1957
1957
Earlier work this paper cites.
G. Dahlquist, Stability and error bounds in the numerical integration of ordinary differential equations , Almqvist & Wiksells, Uppsala, 1958; Transactions of the Royal Institute of Technology, Stockholm, 1959
1959
Earlier work this paper cites.
M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions , Dover Publications INC., 1965
1965
Earlier work this paper cites.
A. I. Markushevich, Theory of functions of a complex variable, Vol. III , Revised English edition translated and edited by Richard A. Silverman, Prenticd-Hall Inc., Englewood Cliffs, N.J., 1967
1967
Earlier work this paper cites.
S. W. Ellacott, Computation of Faber series with application to numerical polynomial approximation in the complex plane , Math. Comp., 40 (1983), pp. 575-587
1983
Earlier work this paper cites.
A. Nauts and R. Wyatt, New approach to many state quantum dynamics: The recurisive residue generation method, Phys. Rev. Lett., 51(1983), pp. 2238-2241
1983
Earlier work this paper cites.
T.J. Park and J.C. Light, Unitary quantum time evolution by iterative Lanczos reduction
1986
Earlier work this paper cites.
L.A. Knizhnerman, Calculation of functions of unsymmetric matrices using Arnoldi’s method, Comput. Math. and Math. Phys., 31 (1991), pp. 1-9
1991
Earlier work this paper cites.
E. Gallopoulos and Y. Saad, Efficient solution of parabolic equations by Krylov approximation methods , SIAM J. Sci. Statist. Comput., 13 (1992), pp. 1236-1264
1992
Cited alongside, same era.
Y. Saad, Analysis of some Krylov subspace approximations to the matrix exponential operator , SIAM J. Numer. Anal., 29 (1992), pp. 209-228
1992
Cited alongside, same era.
V. L. Druskin and L. A. Knizhnerman, Krylov subspace approximations of eigenpairs and matrix functions in exact and computer arithemetic , Numer. Linear Algebra Appl., 2 (1995), pp. 205-217
1995
Cited alongside, same era.
J. Demmel, Applied Numerical Linear Algebra , SIAM, Philadelphia, 1997
1997
Cited alongside, same era.
V. Druskin, A. Greenbaum, and L. Knizhnerman, Using nonorthogonal Lanczos vectors in the computation of matrix functions , SIAM J. Sci. Comput., 19 (1998), pp. 38-54
1998
M. Crouzeix, Numerical range and functional calculus in Hilbert space , Journal of Functional Analysis, 244 (2007), pp. 668-690
2007
Later among the works it cites.
X. Guan, O. Zatsarinny, K. Bartschat, B.I. Schneider, J. Feist, and C.J. Noble, A general approach to few-cycle intense laser interactions with complex atoms
2007
Later among the works it cites.
M. Ilic, I. W. Turner, and V. Anh, Numerical solution of the fractional poisson equations using an adaptively preconditioned Lanczos methods, Journal of Applied Mathematics and Stochastic Analysis, vol. 2008, Article ID 104525, 2008. doi:10.1155/2008/104525
2008
Later among the works it cites.
B. Beckermann and L. Reichel, Error estimates and evaluation of matrix functions via the Faber transform , SIAM J. Numer. Anal., 47 (2009), pp. 3849-3883
2009
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Cited alongside, same era.
M. Benzi and G. H. Golub, Bounds for the entries of matrix functions with applications to preconditioning , BIT, 39 (1999), pp. 417-438
1999
Cited alongside, same era.
C. Moler and C. Van Loan, Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later , SIAM Rev., 45 (2003), pp. 3-49
2003
Cited alongside, same era.
B.I. Schneider and L.A. Collins, The discrete variable method for the solution of the time-dependent Schrödinger equation
2005
Cited alongside, same era.
G. Söderlind, The logarithmic norm. History and modern theory , BIT Numerical Mathematics, 46 (2006), pp. 631-652
2006
Cited alongside, same era.
M. Benzi and N. Razouk, Decay bounds and O(n) algorithms for approximating functions of sparse matrices , Electron. Trans. Numer. Anal., 28 (2007), pp. 16-39
2007
Cited alongside, same era.
2011
Later among the works it cites.
M. Benzi P. Boito and N. Razouk, Decay Properties of Spectral Projectors with Applications to Electronic Structure, SIAM Review, 55 (2013), pp. 3-64
2013
Later among the works it cites.
Q. Ye, Error bounds for the Lanczos methods for approximating matrix exponentials , SIAM J. Numer. Anal., 51 (2013), pp. 66-87
2013
Later among the works it cites.
M. Benzi and P. Boito, Decay Properties for Functions of Matrices over C*-Algebras, Linear Alg. Appl., 456 (2014), pp. 174-198
2014
Later among the works it cites.
M. Benzi and V. Simoncini, Decay Bounds for Functions of Hermitian Matrices with Banded or Kronecker Structure , SIAM J. Matrix Anal. Appl., 36 (2015), pp. 1263-1282
2015
Later among the works it cites.
H. Wang, The Krylov Subspace Methods for the Computation of Matrix Exponentials , Ph.D. Thesis, Department of Mathematics, University of Kentucky, 2015
2015
Later among the works it cites.