@article{Atıcı2026, 
author = {Ferhan M. Atıcı and Amber Wu},
title = {Discrete cosine and sine functions of matrices},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {2},
pages = {1157-1172},
keywords = {matrix valued functions, Putzer algorithm, discrete cosine function, Jordan canonical form, difference equations},
url = {https://www.sciopen.com/article/10.3934/era.2026053},
doi = {10.3934/era.2026053},
abstract = {In this paper, we introduce two methods for constructing matrix-valued cosine and sine functions defined on a discrete domain. The first method develops an algorithm to compute the    n  ×  n matrix-valued cosine and sine of a given square matrix    A with some restrictions on its eigenvalues. The second method derives a formula based on the Jordan canonical form to compute each term of a Jordan block in the discrete matrix-valued cosine and sine of a given square matrix    A. To illustrate the utility of our approach, we present some examples.}
}