Fetching the paper…
Reading the bibliography…
We present $TimeEvolver$, a program for computing time evolution in a generic quantum system.
doi:10.1137/S0036142995280572
M. Hochbruck, C. Lubich, On Krylov Subspace Approximations to the Matrix Exponential Operator, SIAM Journal on Numerical Analysis 34 (5) (1997) 1911–1925 · 1925
Earlier work this paper cites.
doi:10.1090/S0025-5718-1966-0234618-4
S. Kaniel, Estimates for some computational techniques in linear algebra, Math. Comp. 20 (1966) 369–378 · 1966
Earlier work this paper cites.
doi:10.1093/imamat/10.3.373
C. C. Paige, Computational Variants of the Lanczos Method for the Eigenproblem, IMA Journal of Applied Mathematics 10 (3) (1972) 373–381 · 1972
Earlier work this paper cites.
doi:10.1103/PhysRevD.7.2333
J. D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333–2346 · 1973
Earlier work this paper cites.
doi:10.2977/prims/1195192451
H. Takahasi, M. Mori, Double Exponential Formulas for Numerical Integration, Publications of the Research Institute for Mathematical Sciences 9 (3) (1974) 721–741 · 1974
Earlier work this paper cites.
doi:10.1093/imamat/18.3.341
C. C. Paige, Error Analysis of the Lanczos Algorithm for Tridiagonalizing a Symmetric Matrix, IMA Journal of Applied Mathematics 18 (3) (1976) 341–349 · 1976
Earlier work this paper cites.
doi:10.1007/BF02345020
S. W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199–220, [Erratum: Commun. Math. Phys. 46, 206 (1976)] · 1976
Earlier work this paper cites.
doi:10.1016/0024-3795(80)90167-6
C. Paige, Accuracy and effectiveness of the Lanczos algorithm for the symmetric eigenproblem, Linear Algebra and its Applications 34 (1980) 235–258 · 1980
Earlier work this paper cites.
doi:https://doi.org/10.1016/C2013-0-10566-1
P. J. Davis, P. Rabinowitz, Methods of Numerical Integration, 2nd Edition, Academic Press, 1984 · 1984
Earlier work this paper cites.
doi:10.1063/1.451548
T. J. Park, J. C. Light, Unitary quantum time evolution by iterative Lanczos reduction, The Journal of Chemical Physics 85 (10) (1986) 5870–5876 · 1986
Earlier work this paper cites.
doi:10.1145/318789.318793
E. Gallopoulos, Y. Saad, On the Parallel Solution of Parabolic Equations, in: Proceedings of the 3rd International Conference on Supercomputing, ICS ’89, Association for Computing Machinery, New York, NY, USA, 1989, p. 17–28 · 1989
Earlier work this paper cites.
doi:10.1137/0729014
Y. Saad, Analysis of Some Krylov Subspace Approximations to the Matrix Exponential Operator, SIAM Journal on Numerical Analysis 29 (1) (1992) 209–228 · 1992
Earlier work this paper cites.
doi:10.1137/0913071
E. Gallopoulos, Y. Saad, Efficient Solution of Parabolic Equations by Krylov Approximation Methods, SIAM Journal on Scientific and Statistical Computing 13 (5) (1992) 1236–1264 · 1992
Earlier work this paper cites.
doi:10.1007/978-1-4615-2241-6_7
B. Philippe, R. B. Sidje, Transient Solutions of Markov Processes by Krylov Subspaces, in: W. J. Stewart (Ed.), Computations with Markov Chains, Springer US, Boston, MA, 1995, pp. 95–119 · 1995
Cited alongside, same era.
doi:https://doi.org/10.1002/nla.1680020303
V. Druskin, L. Knizhnerman, Krylov subspace approximation of eigenpairs and matrix functions in exact and computer arithmetic, Numerical Linear Algebra with Applications 2 (3) (1995) 205–217 · 1995
Cited alongside, same era.
doi:10.1016/0377-0427(96)00006-4
D. Stewart, T. Leyk, Error estimates for Krylov subspace approximations of matrix exponentials, Journal of Computational and Applied Mathematics 72 (2) (1996) 359 – 369 · 1996
Cited alongside, same era.
doi:10.1016/S0168-9274(97)00033-0
E. Celledoni, I. Moret, A Krylov projection method for systems of ODEs, Applied Numerical Mathematics 24 (2) (1997) 365 – 378, second International Conference on the Numerical Solution of Volterra and Delay Equations · 1997
Cited alongside, same era.
doi:10.1145/285861.285868
R. B. Sidje, Expokit: A Software Package for Computing Matrix Exponentials, ACM Trans. Math. Softw. 24 (1) (1998) 130–156 · 1998
Cited alongside, same era.
G. Dvali, L. Eisemann, M. Michel, S. Zell, Black hole metamorphosis and stabilization by memory burden, Phys. Rev. D 102 (10) (2020) 103523 · 2006
Later among the works it cites.
doi:10.4171/067
C. Lubich, From Quantum to Classical Molecular Dynamics: Reduced Models and Numerical Analysis, European Mathematical Society, 2008 · 2008
Later among the works it cites.
doi:10.1109/EUMC.2008.4751704
S. Velamparambil, S. MacKinnon-Cormier, J. Perry, R. Lemos, M. Okoniewski, J. Leon, GPU Accelerated Krylov Subspace Methods for Computational Electromagnetics, in: 2008 38th European Microwave Conference, 2008, pp. 1312–1314 · 2008
Later among the works it cites.
doi:10.1137/110820191
M. A. Botchev, V. Grimm, M. Hochbruck, Residual, Restarting, and Richardson Iteration for the Matrix Exponential, SIAM Journal on Scientific Computing 35 (3) (2013) A1376–A1397 · 2013
Later among the works it cites.
doi:10.1137/11085935X
Q. Ye, Error Bounds for the Lanczos Methods for Approximating Matrix Exponentials, SIAM Journal on Numerical Analysis 51 (1) (2013) 68–87 · 2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
doi:10.1137/S1064827596303661
V. Druskin, A. Greenbaum, L. Knizhnerman, Using Nonorthogonal Lanczos Vectors in the Computation of Matrix Functions, SIAM Journal on Scientific Computing 19 (1) (1998) 38–54 · 1998
Cited alongside, same era.
doi:10.1137/S1064827595295337
M. Hochbruck, C. Lubich, H. Selhofer, Exponential Integrators for Large Systems of Differential Equations, SIAM Journal on Scientific Computing 19 (5) (1998) 1552–1574 · 1998
Cited alongside, same era.
doi:10.1137/1.9781611971163
B. N. Parlett, The Symmetric Eigenvalue Problem, Society for Industrial and Applied Mathematics, 1998 · 1998
Cited alongside, same era.
doi:10.1016/S0377-0427(00)00501-X
M. Mori, M. Sugihara, The double-exponential transformation in numerical analysis, Journal of Computational and Applied Mathematics 127 (1) (2001) 287–296 · 2001
Cited alongside, same era.
doi:10.1137/1.9780898718027
N. J. Higham, Accuracy and Stability of Numerical Algorithms, 2nd Edition, Society for Industrial and Applied Mathematics, 2002 · 2002
Cited alongside, same era.
doi:10.1137/1.9780898718003
Y. Saad, Iterative Methods for Sparse Linear Systems, 2nd Edition, Society for Industrial and Applied Mathematics, 2003 · 2003
Cited alongside, same era.
doi:10.1080/10586458.2005.10128931
D. H. Bailey, K. Jeyabalan, X. S. Li, A comparison of three high-precision quadrature schemes, Experimental Mathematics 14 (3) (2005) 317–329 · 2005
Cited alongside, same era.
G. Dvali, C. Gomez, Black Holes as Critical Point of Quantum Phase Transition, Eur. Phys. J. C 74 (2014) 2752 · 2014
Later among the works it cites.
Z. Jia, H. Lv, A posteriori error estimates of Krylov subspace approximations to matrix functions, Numerical Algorithms 69 (1) (2015) 1–28 · 2015
Later among the works it cites.
H. Wang, Q. Ye, Error Bounds for the Krylov Subspace Methods for Computations of Matrix Exponentials, SIAM Journal on Matrix Analysis and Applications 38 (1) (2017) 155–187 · 2017
Later among the works it cites.
M. Brenes, V. Varma, A. Scardicchio, I. Girotto, Massively parallel implementation and approaches to simulate quantum dynamics using Krylov subspace techniques, Computer Physics Communications 235 (2019) 477–488 · 2018
Later among the works it cites.
G. Dvali, M. Michel, S. Zell, Finding Critical States of Enhanced Memory Capacity in Attractive Cold Bosons, EPJ Quant. Technol. 6 (2019) 1 · 2019
Later among the works it cites.
S. Paeckel, T. Köhler, A. Swoboda, S. R. Manmana, U. Schollwöck, C. Hubig, Time-evolution methods for matrix-product states, Annals of Physics 411 (2019) 167998 · 2019
Later among the works it cites.
T. Jawecki, W. Auzinger, O. Koch, Computable upper error bounds for Krylov approximations to matrix exponentials and associated φ \varphi -functions, BIT Numerical Mathematics 60 (2020) 157–197 · 2020
Later among the works it cites.