留数定理在计算矩阵函数值中的应用

The application of residue theorem in calculation of matrix function value

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={a ij}∈Cn×n,‖A‖为相容矩阵范数,L是一半径充分大的圆周(半径r≥‖A‖),(ξI-A)-1={bij(ξ)},则有f(A)={1/(2πi)∫ L乙f(ξ)bij(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.

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