Abstract
In this paper we define a natural generalization of ordinary continued fractions and refractions (de Bruin [2]). This so-called general n-fraction is associated with a first-order recurrence system, and we look at some of its applications: computation of eigenvectors, stable computation of non-dominant solutions of recurrence systems, and calculation of vector rational interpolants.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Agarwal R.P.: 1992, Difference equations and inequalities: theory, methods and applications, Marcel Dekker, Inc., New York.
de Bruin M.G.: 1974, Generalized continued fractions and a multidimensional Padé Table, Doctoral Thesis, Amsterdam.
de Bruin M.G., Jacobsen L.: 1987, ‘Modification of Generalised Continued Fractions I’, Lecture Notes in Math. (J. Gilewicz et al. Eds), Springer-Verlag, Berlin, pp. 161–176.
Gautschi W.: 1967, ‘Computational Aspects of Three-Term Recurrence Relations’,SIAM Review Vol. 9, pp. 24–82.
Jones W.B., Thron W.J.: 1980, Continued Fractions: Analytic Theory and Applications, Encyclopedia of Mathematics 11, Addison-Wesley Publishing Company, Reading, Mass..
Levrie P., Jacobsen L.: 1988, ‘Convergence Acceleration for Generalized Continued Fractions’,Trans. Amer. Math. Soc. Vol. 305no. 1, pp. 263–275.
Levrie P., Bultheel A.: 1993, ‘A note on Thiele n-fractions’, Numer. Algorithms Vol. 4, pp. 225–239.
Lorentzen L., Waadeland H.: 1992, Continued Fractions with Applications, North-Holland, Amsterdam.
Mattheij R.M.M.: 1980, ‘Characterizations of Dominant and Dominated Solutions of Linear Recursions’, Numer. Math. Vol. 35, pp. 421–442.
Mattheij R.M.M.: 1982, ‘Stable Computation of Solutions of Unstable Linear Initial Value Recursions’, BIT Vol. 22, pp. 79–93.
Milne-Thomson L.M.: 1933, The calculus of finite differences, MacMillan.
Perron 0.: 1917, ’über Systeme von Linearen Differenzengleichungen erster Ordnung’,J. Reine Angew. Math. Vol. 147, pp. 36–53.
Van Bard M., Bultheel A.: 1990, ‘A New Approach to th Rational Interpolation Problem: the Vector Case’, J. Comp. Appl. Math. Vol. 33, pp. 331–346.
Van der Cruyssen P.: 1979, ‘Linear Difference Equations and Generalized Continued Fractions’, Computing Vol. 22, pp. 269–278.
Wimp J.: 1984, Computation with Recurrence Relations, Pitman Advanced Publishing Program, Pitman Publishing Inc., Boston.
Zahar R.V.M.: 1990, ‘A Generalization of Olver’s Algorithm for Linear Difference Systems’, in Asymptotic and Computational Analysis (R. Wong ed.), Marcel Dekker, Inc., New York, pp. 535–551.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1994 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Levrie, P., Van Barel, M., Bultheel, A. (1994). First-Order Linear Recurrence Systems and General N-Fractions. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation II. Mathematics and Its Applications, vol 296. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0970-3_33
Download citation
DOI: https://doi.org/10.1007/978-94-011-0970-3_33
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4420-2
Online ISBN: 978-94-011-0970-3
eBook Packages: Springer Book Archive