New vector forms of elemental functions with Taylor series. (Q1408319)

A general formula for the vector form of any elementary function making use of a Taylor series expansion is proved. This formula is further specialized for particular elementary functions. The need to approximate solutions of large stiff ordinary differential equations by matrix exponentials leads to a big amount of computational work when using for instance Krylov subspace methods. The usage of the vector form of elementary functions can lead to an essential reduction of this work achieving the same goal.