CAJ | 학술논문

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}∈Cn×n，丨丨A丨丨为相容矩阵范数，L是一半径充分大的圆周（半径r≥丨丨A丨丨）,（ξI-A）-1＝{bij（ξ）}，则有f（A）={1/（12πi）Lf（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。
문중탐토료구진함수치적계산문제。증명료：약f（z）시복평면C상적정함수，A={aij}∈Cn×n，곤곤A곤곤위상용구진범수，L시일반경충분대적원주（반경r≥곤곤A곤곤）,（ξI-A）-1＝{bij（ξ）}，칙유f（A）={1/（12πi）Lf（ξ）bij（ξ）dξ}。의거해결론，문중급출료이용류수래계산구진함수치적신방법。
This paper discusses the calculation problem of matrix function value. It is proved that if f (z) is an entire function on the complex plane C, A={aij}∈Cn×n, A is the compatible norm, L is a circle for which the radius is large enough(r≥ A ),(ξI-A)-1={bij(ξ)}, then f(A)={ 12πi Lf(ξ)bij(ξ)dξ} holds. According to this formula, it presents a new cheaper method to calculate matrix function value by using residue theorem.