An improved algorithm for factoring linear ordinary differential operators

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An improved algorithm for factoring linear ordinary differential operators

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the international symposium on Symbolic and algebraic computation table of contents

Oxford, United Kingdom

Pages: 336 - 340

Year of Publication: 1994

ISBN:0-89791-638-7

Author

Manuel Bronstein

Wissenschaftliches Rechnen, ETH - Zentrum, CH-8092 Zürich, Switzerland

Sponsor

SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 0, Downloads (12 Months): 21, Citation Count: 14

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ABSTRACT

We describe an efficient algorithm for computing the associated equations appearing in the Beke-Schlesinger factorisation method for linear ordinary differential operators. This algorithm, which is based on elementary operations with sets of integers, can be easily implemented for operators of any order, produces several possible associated equations, of which only the simplest can be selected for solving, and often avoids the degenerate case, where the order of the associated equation is less than in the generic case. We conclude with some fast heuristics that can produce some factorisations while using only linear computations.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

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	A. Ronveaux, Factorization of the Heun's differential operator, Applied Mathematics and Computation, v.141 n.1, p.177-184, 20 August 2003
	Ziming Li , Fritz Schwarz , Serguei P. Tsarev, Factoring zero-dimensional ideals of linear partial differential operators, Proceedings of the 2002 international symposium on Symbolic and algebraic computation, p.168-175, July 07-10, 2002, Lille, France
	Ruben Debeerst , Mark van Hoeij , Wolfram Koepf, Solving differential equations in terms of bessel functions, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, July 20-23, 2008, Linz/Hagenberg, Austria
	Anne Fredet, Factorization of linear differential operators in exponential extensions, Proceedings of the 2003 international symposium on Symbolic and algebraic computation, p.103-110, August 03-06, 2003, Philadelphia, PA, USA
	M. V. Sosnin, An Algorithm for Nonparametric Decomposition of Differential Polynomials, Programming and Computing Software, v.27 n.1, p.43-49, January-February 2001
	Xiao-Shan Gao , Mingbo Zhang, Decomposition of differential polynomials with constant coefficients, Proceedings of the 2004 international symposium on Symbolic and algebraic computation, p.175-182, July 04-07, 2004, Santander, Spain
	S. P. Tsarev, Symbolic manipulation of integrodifferential expressions and factorization of linear ordinary differential operators over transcendental extensions of a differential field, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.310-315, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Ziming Li , Fritz Schwarz , Serguei P. Tsarev, Factoring systems of linear PDEs with finite-dimensional solution spaces, Journal of Symbolic Computation, v.36 n.3-4, p.443-471, September 2003
	Sergey P. Tsarev, Generalized laplace transformations and integration of hyperbolic systems of linear partial differential equations, Proceedings of the 2005 international symposium on Symbolic and algebraic computation, p.325-331, July 24-27, 2005, Beijing, China
	S. P. Tsarev, On factorization of nonlinear ordinary differential equations, Proceedings of the 1999 international symposium on Symbolic and algebraic computation, p.159-164, July 28-31, 1999, Vancouver, British Columbia, Canada
	S. P. Tsarev, An algorithm for complete enumeration of all factorizations of a linear ordinary differential operator, Proceedings of the 1996 international symposium on Symbolic and algebraic computation, p.226-231, July 24-26, 1996, Zurich, Switzerland
	Eckhard Pflügel, An algorithm for computing exponential solutions of first order linear differential systems, Proceedings of the 1997 international symposium on Symbolic and algebraic computation, p.164-171, July 21-23, 1997, Kihei, Maui, Hawaii, United States
	Johannes Grabmeier , Erich Kaltofen , Volker Weispfenning, Cited References, Computer algebra handbook, Springer-Verlag New York, Inc., New York, NY, 2003