Evaluation of branched continued fractions using block-tridiagonal linear systems

Abstract

The convergent of an ordinary continued fraction can be computed by solving a tridiagonal linear system for its first unknown. In this paper, this approach is generalized to branched continued fractions, and it is shown how the convergent of a branched continued fraction can be considered as the first unknown of a block-tridiagonal linear system. Hence algorithms for the solution of such systems of equations can be used for the computation of convergents of branched continued fractions, which have applications in approximation theory, systems theory, etc. In future research, special attention will be paid to the use of parallel algorithms. © 1988 Oxford University Press.