No abstract

No abstract

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. This algorithm is a modification of some well known and widely used algorithms. A novel feature is an approximate calculation of divided differences for the Newton interpolating polynomial in a special way. This modification does not require to reorder the Schur triangular form and to solve Sylvester equations.

It is well known that the equation x ′ (t) = Ax(t) + f (t), where A is a square matrix, has a unique bounded solution x for any bounded continuous free term f , provided the coefficient A has no eigenvalues on the imaginary axis. This solution can be represented in the form

No abstract