中文摘要：

文中探讨了矩阵函数值的计算问题．证明了：若f（z）是复平面C上的整函数，A={aij}∈Cnxn｜｜A｜｜为相容矩阵范数，L是一半径充分大的圆周（半径r≥｜｜A｜｜）,（ζI-A）^-1={bij（ζ）}，则有f（A）={1/2πi∫Lf（ξ）by（ξ）dξ}。依据该结论，文中给出了利用留数来计算矩阵函数值的新方法。

英文摘要：

This paper discusses the calculation problem of matrix function value. It is proved that iff （z） is an entire function on the complex plane C, A={aij}∈Cnxn｜｜A｜｜ is the compatible norm, L is a circle for which the radius is large enough（rr≥｜｜A｜｜）,（ζI-A）^-1={bij（ζ）},than f（A）={1/2πi∫Lf（ξ）by（ξ）dξ} holds. According to this formula, it presents a new cheaper method to calculate matrix function value by using residue theorem