ABSTRACT
The Padé-Lanczos approximant (PLA) is a hybrid method with two steps consisting of: the Lanczos tridiagonalization of the original large matrix and the subsequent inversion of the sparse Jacobi matrix by means of the Padé approximant (PA). For any given Green function, its PLA of a fixed order is unique and, hence, the same result must be obtained irrespective of the method used to generate the numerator and denominator polynomials. This chapter applies a different procedure to evaluate the Green function within the usual PA without the Lanczos algorithm. It also proves that the Maclaurin series of the Green function in powers of with the auto-correlation functions or time signal points as the expansion coefficients, is mathematically equivalent to the PLA.
