Geometric Numerical
Integration and Applications
An optimized algorithm for computing
the exponential of skew-Hermitian matrices
In the paper
- P. Bader, S. Blanes, F. Casas, and M. Seydaoglu.
An efficient algorithm to compute the exponential of skew-Hermitian matrices for the time integration of the Schrödinger equation.
Mathematics and Computers in Simulation 194
(2022), 383-400
a new algorithm is proposed
to approximate in a very efficient way the exponential of
skew-Hermitian matrices. It is based on the evaluation of
Chebyshev polynomial of matrices. For problems of the form
exp(-i A), with A a real and symmetric matrix, an improved
version is presented which allows one to compute the sine and
cosine of A with a much reduced computational cost.
We have implemented the procedure as different Matlab functions,
which in any case offer a superior efficiency than the standard
function expm.
Additional information is collected here, and the codes
are the following:
- expmC.m: the new
algorithm based on Chebyshev polynomials to compute the exponential
of skew-Hermitian matrices
- cosmsinmC.m: algorithm based on Chebyshev
polynomials to compute
simultaneously cos(A) and sin(A) when A is a real and
symmetric matrix
- Example_0.m: a simple example where the
previous functions can be applied