Advances in the Approximation of the Matrix Hyperbolic Tangent

In this paper, we introduce two approaches to compute the matrix hyperbolic tangent. While one of them is based on its own definition and uses exponential, other focused expansion Taylor series. For second approximation, analyse different alternatives evaluate corresponding polynomials. This resulted in three stable accurate codes, which implemented MATLAB numerically computationally compared by means a battery tests composed distinct state-of-the-art matrices. Our results show that series-based methods were more accurate, although somewhat expensive, with approach exponential matrix. To avoid drawback, propose use set formulas allows us polynomials efficient way traditional Paterson–Stockmeyer method, thus, substantially reducing number products (practically equal exponential), without penalising accuracy result.