Discrete cosine and sine functions of matrices
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 \times 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.
Fields of Study & Subjects
Matrix Theory and Algorithms
Numerical methods for differential equations
Mathematical and Computational Methods
Publication details
- Journal / source
- Electronic Research Archive
- Volume
- 34
- Issue
- 2
- Pages
- 1157–1172
- Publication date
- 1 January 2026