Linear difference equations and generalized continued fractions
Copyright policy )Linear difference equations and generalized continued fractions
In one of his papers [5] Gautschi presents an algorithm for determining the minimal solution of a second-order homogeneous difference equation. The method is based on the connection between the existence of a minimal solution of such a difference equation and the convergence of a certain continued fraction. In the present paper, these results are generalized. For this purpose we use the concept of generalized continued fraction. The resulting algorithm is suitable for solving (n+1)-th order recursions (n≥1) for which there existn independent solutions that are dominated by each solution that does not belong to the space spanned by thesen solutions.
- University of Antwerp Belgium
Minimal Solution, Numerical methods for functional equations, Convergence and divergence of continued fractions, Additive difference equations, Generalized Continued Fraction, Second-Order Homogeneous Difference Equation
Minimal Solution, Numerical methods for functional equations, Convergence and divergence of continued fractions, Additive difference equations, Generalized Continued Fraction, Second-Order Homogeneous Difference Equation
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