ABSTRACT
This chapter develops a recursive algorithm for solving a tridiagonal inhomogeneous system of linear equations. It solves the system of linear equations by the Gaussian elimination method. The chapter introduces two auxiliary vectors for obtaining the general recursion for the solution of the system of linear equations. It analyses the application of Lanczos continued fraction to the quantification problem (harmonic inversion) with the goal of determining the key spectral parameters while recalling that the Lanczos continued fraction is equivalent to the Padé–Lanczos approximant.
