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