Algorithms: economical computation of functions of real matrices

An algorithm is presented which economizes on the calculation of F(a), where A is a real matrix and F(x) a real valued function of x, using spectral analysis. Assuming the availability of the software for the calculation of the complete set of eigenvalues and eigen vectors of A, it is shown that the complex matrix arithmetics involved in subsequent operations leading from A to F(A) can be reduced to the size comparable with the analogous problem in real matrix arithmetics. Saving in CPU time and storage has been achieved by utilizing explicitly the property that complex eigenvalues of a real matrix appear in pairs of complex conjugated numbers. (author)