函数值Padé-型逼近已被应用于求第二类Fredholm 积分方程的逼近解. 函数值Padé-型逼近存在的首要条件是Hankel 行列式不为0, 为避免这一条件的限制, 给出一种新的函数值Padé-Frobenius 逼近的定义及构造. 通过分析Toeplitz 矩阵核结构的特征, 给出了一种分母次数最低的函数值Padé-Frobenius 逼近的算法, 从而拓宽了求第二类Fredholm 积分方程逼近解的范围. 最后, 通过数值实例证明了该方法的有效性.

Function-valued Padé-type approximation (FPTA) was applied to solve the Fredholm integral equations of the second kind. To avoid the constraint that the determinant of Hankel cannot equal to zero for FPTA, a definition and its construction of a function-valued Padé-Frobenius approximation (FPFA) is given. By studying the kernel structure of the Toeplitz matrix, an algorithm is presented for the function-valued Padé-Frobenious approximation with reduced denominator. Thus the application range of approximation solution of the integral equations is developed. Finally, an example is given to show effectiveness of the method.