Incomplete Cross Splitting in the Approximation of Skew-Symmetric Matrix Exponential

This paper proposes a new splitting method for approximating the exponential of skew-symmetric and skew-Hermitian matrix A . Our point of departure is the splitting methods for approximation of the matrix exponential, which we modify and combine with new low-cost analytic formula for some sparse matrix exponential. Our motivation is to create and test a fast exponential approximation method in the context of a balance between speed and quality of approximation. We propose a cross splitting of the matrix A and use it in incomplete form for reducing computational complexity of exponential stage. We have also derived an analytical formula for a cross-type sparse skew-symmetric and skew-Hermitian matrix exponential, similar to the Euler-Rodrigues relation, well known for skew-symmetric matrices in R 3 . We evaluate this approximation problem in the context of computational cost and the speed of the algorithms used in technology. A number of numerical experiments conclude the optimization problem of the Independent Components Analysis type, the results of which confirm the effectiveness of the proposed method in technical applications.