Computing the matrix sine and cosine simultaneously with a reduced number of products

TL;DR

This paper introduces a new Taylor polynomial-based method for simultaneously computing matrix sine and cosine with fewer matrix products, improving efficiency over Padé-based schemes in various precision settings.

Contribution

The paper develops reduced-product algorithms for matrix sine and cosine using Taylor approximations, enhancing computational efficiency over existing Padé-based methods.

Findings

More efficient than Padé-based schemes in various norms.

Applicable in both single and double precision arithmetic.

Reduces computational cost by decreasing matrix products.

Abstract

A new procedure is presented for computing the matrix cosine and sine simultaneously by means of Taylor polynomial approximations. These are factorized so as to reduce the number of matrix products involved. Two versions are developed to be used in single and double precision arithmetic. The resulting algorithms are more efficient than schemes based on Pad\'e approximations for a wide range of norm matrices.