Validity and error analysis of calculating matrix exponential function and vector product

Abstract

Abstract In this study, an efficient calculation method of matrix exponential function and vector product is proposed to reduce the calculation error. This method is based on the flexible exponential integral scheme; using B-series theory and two-color tree theory, the numerical series expression is obtained, and the exponential integral of the matrix exponential function is solved. By constructing a specific numerical integration scheme and analyzing its convergence under the theoretical framework of analytic semigroups, the convergence analysis of numerical schemes is studied and perfected. The numerical results show that the proposed method of matrix exponential function and vector product has a small error, which shows obvious advantages in reducing the calculation error.