# Calculating elements of matrix functions using divided differences

@article{Barash2022CalculatingEO, title={Calculating elements of matrix functions using divided differences}, author={Lev Yu. Barash and Stefan G{\"u}ttel and Itay Hen}, journal={Comput. Phys. Commun.}, year={2022}, volume={271}, pages={108219} }

## Figures and Tables from this paper

## One Citation

### Computational graphs for matrix functions

- Computer ScienceArXiv
- 2021

The Julia package GraphMatFun.jl offers the tools to generate and manipulate computational graphs, to optimize their coe cients, and to generate Julia, MATLAB, and C code to evaluate them e ciently.

## References

SHOWING 1-10 OF 36 REFERENCES

### Off-diagonal series expansion for quantum partition functions

- Physics
- 2018

We derive an integral-free thermodynamic perturbation series expansion for quantum partition functions which enables an analytical term-by-term calculation of the series. The expansion is carried out…

### Permutation matrix representation quantum Monte Carlo

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2020

We present a quantum Monte Carlo algorithm for the simulation of general quantum and classical many-body models within a single unifying framework. The algorithm builds on a power series expansion of…

### The Ising model with a transverse field. II. Ground state properties

- Physics
- 1971

For Pt. I see ibid., vol. 4, 2359 (1971). The properties of the Ising model with a transverse field, with the Hamiltonian written H=- Gamma Sigma iSix-1/2 Sigma i,jJijSizSjz, are studied by…

### Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection

- Computer Science, Chemistry
- 2013

This work reviews various rational Krylov methods for the computation of large‐scale matrix functions and focuses on the rational Arnoldi method and variants thereof, namely, the extended Krylov subspace method and the shift‐and‐invert Arnoldi methods.

### Evaluating Matrix Functions by Resummations on Graphs: The Method of Path-Sums

- MathematicsSIAM J. Matrix Anal. Appl.
- 2013

We introduce the method of path-sums, which is a tool for analytically evaluating a primary function of a finite square discrete matrix based on the closed-form resummation of infinite families of…

### Ising model in a transverse field. I. Basic theory

- Physics
- 1973

A brief review is first made of systems for which the spin-iIsing model in a transverse field provides a useful description (insulating magnetic systems, order-disorder ferroelectrics, cooperative…

### Topical Issue Applied and Numerical Linear Algebra (2/2)

- Computer ScienceGAMM-Mitteilungen
- 2020

The present special issue of the GAMM Mitteilungen, which is the second of a two-part series, contains contributions on the topic of Applied and Numerical Linear Algebra, compiled by the GAMM…

### The Calculus of Observations: a Treatise on Numerical Mathematics

- MathematicsNature
- 1924

A SET of numerical data, whether obtained from theory or experiment, gives rise to mathematical problems of interest and importance. The consideration of these problems now forms an important branch…

### Network Properties Revealed through Matrix Functions

- Computer ScienceSIAM Rev.
- 2010

A general class of measures based on matrix functions is introduced, and it is shown that a particular case involving a matrix resolvent arises naturally from graph-theoretic arguments.

### Eigenspaces for Graphs

- Computer ScienceInt. J. Image Graph.
- 2002

The feasibility of using graph-based descriptions to learn the view structure of 3D objects is investigated and how multidimensional scaling may be used to generate eigenspaces from a set of pairwise distances between graphs is investigated.