Expokit: a software package for computing matrix exponentials
Open accessAbstract
Expokit provides a set of routines aimed at computing matrix exponentials. More precisely, it computes either a small matrix exponential in full, the action of a large sparse matrix exponential on an operand vector, or the solution of a system of linear OBEs with constant inhomogeneity. The backbone of the sparse routines consists of matrix-free Krylov subspace projection methods (Arnoldi and Lanczos processes), and that is why the toolkit is capable of coping with sparse matrices of large dimension. The software handles real and complex matrices and provides specific routines for symmetric and Hermitian matrices. The computation of matrix exponentials is a numerical issue of critical importance in the area of Markov chains and furthermore, the computed solution is subject to probabilistic constraints. In addition to addressing general matrix exponentials, a distinct attention is assigned to the computation of transient states of Markov chains.
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The algorithm differs from one-site DMRG by replacing the optimization step with an evolution step and adding an extra evolution step for the zero-site center before absorbing it at the next site.
“Having a Lanczos routine for computing the matrix exponential acting on a vector (e.g., Ref. [31]), this algorithm differs from one-site DMRG by replacing the optimization step for A C (n) (eigenvalue solver) with the evolution step, and by adding an extra evolution step for C(n) before absorbing it at the next site.”
From Unifying time evolution and optimization with matrix product states (2016) · cites this paper as [31]
The time-dependent variational principle has enabled time-dependent variational Monte Carlo calculations for bosons and strongly correlated fermions.
“The time-dependent variational principle (TDVP) 167-169 has enabled time-dependent variational Monte Carlo calculations for bosons 170 and strongly correlated fermions 171 .”
From Quantum Chemistry in the Age of Quantum Computing (2019) · cites this paper as [167]
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- Authors
- Sidje, R. B.
- Affiliations
- The University of Queensland (AU)
- Corresponding author
- Sidje, Roger B.
- ORCID
- Sidje, Roger B.
- Venue
- ACM Transactions on Mathematical Software
- Published
- 1998-03
- Volume
- 24
- Issue
- 1
- Pages
- 130-156
- ISSN
- 0098-3500 (ISSN-L)
- 1557-7295
- OpenAlex
- W2130727150
- Cited by
- 781
- References
- 35
- Citations by year
- 2026: 13 · 2025: 21 · 2024: 28 · 2023: 21 · 2022: 24 · 2021: 43 · 2020: 33 · 2019: 38 · 2018: 43 · 2017: 47 · 2016: 48 · 2015: 38 · 2014: 45 · 2013: 39 · 2012: 44
- FWCI
- 6.54
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- ACM Transactions on Mathematical Software (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
- Physical Sciences › Mathematics › Numerical Analysis › Numerical methods for differential equations
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Numerical Methods and Algorithms
- Keywords
- matrix exponential, sparse matrices, matrix-free methods, Krylov subspace projection, Arnoldi method, Lanczos method, linear ordinary differential equations, Markov chains, transient states, Hermitian matrices, software library
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