Continued fraction solutions to systems of linear equations
Sanhita Swain · Journal of Physics A Mathematical and General · 1976
Solutions of systems of linear equations or linear recurrence relations are obtained in the form of series of products of continued fractions. Simple rules are presented for obtaining the series of any given problem. The continued fraction expansion is superior to ordinary perturbation theory; each continued fraction represents a partial summation of the ordinary perturbation series. The use of the method in eigenvalue problems, and its possible application in numerical analysis are discussed.