Abstract: 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.

Key words: determinant of Hankel, Fredholm integral equation, function-valued Pad´e-Frobenius approximation, Toeplitz matrix