Generalized Polar Decompositions in Matrix Exponential

摘要

Matrix exponential, computation is a difficulty thing when the order of the matrix get big and big after discretion. When we use Lie group method to get numeric solution of a differential equation, we often face this problem.Li group method is a kind of prosperous method, its basic ideas is to keep the numeric solution in a manifold which is less than the Euclid space while bigger than the analytic solution manifold, so we can get more exact numeric solution than other method. So we discussed the generalized polar decompositions method for matrix exponential.