矩阵函数计算的插值多项式方法

Interpolation Polynomial Method for Calculation of Matrix Functions

矩阵函数是数学专业课程中的重要内容之一,也是部分非数学类专业课程中的内容.关于矩阵函数符号计算的传统教学方法,是借助矩阵的Jordan标准形,这种方法需要求出矩阵到Jordan标准形的过渡矩阵,运算相对复杂.利用插值多项式计算矩阵函数的方法,可以避开计算过渡矩阵,节省教学时间,并能起到很好的教学效果.

Matrix functions is an important tool in mathematics and engineering.In classical textbooks,the method for calculation of matrix functions is by using of Jordan canonical forms.This method is usually complicated,since the transition matrix is required,which is not easy to be found.By using of interpolation polynomial,the values of matrix functions can be found without using transition matrices.In practice,it is proved that interpolation polynomial method is easily accepted by students.