Continued fraction expansion and inversion by ‘rearranged’ Routh tables

Abstract

The Routh algorithm is known to be the simplest method for continued fraction expansion and inversion but it faces a serious limitation when the first column entry of any row of the Routh table becomes zero (but not a zero row). In this paper a remedy for such situations is proposed by rearranging the coefficients of the row in which zero entry has occurred in the first column of the Routh table. All possible cases, where the first column entry of the Routh table may become zero, are discussed for Cauer's first and second forms and are illustrated by numerical examples. The coefficients of the rearranged Routh table are also calculated by the usual Routh algorithm, hence it is equally suitable for digital computation.