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.

翻译：让 $T 成为真实频谱的平方矩阵, 让 $f 成为分析函数 。 正在讨论 $f( T) 的大致计算问题。 应用 Schur 三角分解和重新排序, 可以假设$T 是三角的, 其对角条目 $t ⁇ ii} 美元是按不断增长的顺序排列的。 为避免使用差异 $t ⁇ ii}- t ⁇ jj} 美元进行计算, 接近( 包括) $t ⁇ ii} 和 $t ⁇ jj} 美元, 建议以块形式代表$T 美元, 并使用内插多位数计算两个主要区块对角。 $f( T) 其余的条目可以使用 Parlett 重现算法计算 。 还建议用扩大的位数进行 scalal 操作( 如建立 内插多位数 ) 。