ABSTRACT
This chapter deals with Lanczos continued fractions (LCF). A general continued fraction (CF) is another way of writing the PA as a staircase with descending quotients. There are several equivalent symbolic notations in use for a given CF. The LCF as a versatile convergence accelerator can yield the frequency spectrum with a reduced number of terms {αn, βn}. The meaning of the nearest neighbour approximation within the LCF is that the coefficients {αn, βn} become increasingly less significant for determination of the Green function as one progresses further down the continued fraction. The chapter shows that the nth order LCF is mathematically equivalent to the Padé-Lanczos approximant.
