An Estimate of Approximation of an Analytic Function of Two Matrices by a Polynomial.

Let be open convex sets, and , , and , , be (maybe repetitive) points. Let be an analytic function. Let the interpolating polynomial be determined by the values of on the rectangular grid , , . Let and be matrices of the sizes and , respectively. The function of and can be defined by the formula where and surround the spectra and , respectively; is defined in the same way. An estimate of is given. [ABSTRACT FROM AUTHOR]