Calculating a function of a matrix with a real spectrum

Let T be a square matrix with real spectrum, and let f an analytic function. The problem of the approximate calculation f(T) is discussed. Applying Schur triangular decomposition reordering, one can assume that its diagonal entries tii are arranged in increasing order. To avoid calculations using differences − tjj close (including equal) tjj, it proposed to represent block form calculate two main diagonals interpolating polynomials. rest calculated Parlett recurrence algorithm. It also perform some scalar operations (such as building polynomials) enlarged number significant decimal digits.