On Bernoulli series approximation for the matrix cosine - Defez, Emilio; Ibáñez, Javier; Alonso, José M.; Alonso‐Jordá, Pedro (Mathematical methods in the applied sciences, 2022)
This paper presents a new series expansion based on Bernoulli matrix polynomials to approximate the matrix cosine function. An approximation based on this series is not a straightforward exercise since there exist different options to implement such a solution. We dive into these options and include a thorough comparative of performance and accuracy in the experimental results section that shows benefits and downsides of each one. Also, a comparison with the Padé approximation is included. The algorithms have been implemented in MATLAB and in CUDA for NVIDIA GPUs.