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An algorithm for computing an analytic function of a matrix $A$ is described.The algorithm is intended for the case where $A$ has some close eigenvalues,and clusters (subsets) of close eigenvalues are separated from each other. Thisalgorithm is a modification of some well known and widely used algorithms. Anovel feature is an approximate calculation of divided differences for theNewton interpolating polynomial in a special way. This modification does notrequire to reorder the Schur triangular form and to solve Sylvester equations.

Computation of a function of a matrix with close eigenvalues by means of the Newton interpolating polynomial