Computing super-irreducible forms of systems of linear differential equations via moser-reduction

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Computing super-irreducible forms of systems of linear differential equations via moser-reduction: a new approach

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International Conference on Symbolic and Algebraic Computation archive
Proceedings of the 2007 international symposium on Symbolic and algebraic computation table of contents

Waterloo, Ontario, Canada

SESSION: Contributed papers table of contents

Pages: 1 - 8

Year of Publication: 2007

ISBN:978-1-59593-743-8

Authors

Moulay A. Barkatou	Université de Limoges, Limoges, France
Eckhard Pflügel	Kingston University, Kingston upon Thames, Surrey, United Kingdom

Sponsors

ACM: Association for Computing Machinery
SIGSAM: ACM Special Interest Group on Symbolic and Algebraic Manipulation

Publisher

ACM New York, NY, USA

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Downloads (6 Weeks): 4, Downloads (12 Months): 16, Citation Count: 2

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ABSTRACT

The notion of irreducible forms of systems of linear differential equations as defined by Moser [14 ] and its generalisation, the super-irreducible forms introduced by Hilali/Wazner in [9 ] are important concepts in the context of the symbolic resolution of systems of linear differential equations [3,15,16 ]. In this paper, we give a new algorithm for computing, given an arbitrary linear differential system with formal power series coefficients as input, an equivalent system which is super-irreducible. Our algorithm is optimal in the sense that it computes transformation matrices which obtain a maximal reduction of rank in each step of the algorithm. This distinguishes it from the algorithms in [9,14,2] and generalises [7].

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.

	1	M. Barkatou. An algorithm for computing a companion block diagonal form for a system of linear differential equations. Journal of App. Alg. in Eng. Comm. and Comp., 4, 1993.
	2	A. Barkatou, A rational version of Moser's algorithm, Proceedings of the 1995 international symposium on Symbolic and algebraic computation, p.297-302, July 10-12, 1995, Montreal, Quebec, Canada [doi>10.1145/220346.220385]
	3	M. Barkatou. An algorithm to compute the exponential part of a formal fundamental matrix solution of a linear differential system. Journal of App. Alg. in Eng. Comm. and Comp., 8(1):1--23,1997.
	4	M. A. Barkatou, On super-irreducible forms of linear differential systems with rational function coefficients, Journal of Computational and Applied Mathematics, v.162 n.1, p.1-15, 1 January 2004 [doi>10.1016/j.cam.2003.08.020]
	5	M. Barkatou and E. Pügel. The ISOLDE package. A SourceForge Open Source project, http://isolde.sourceforge.net 2006.
	6	G. Chen, An algorithm for computing the formal solutions of differential systems in the neighborhood of an irregular singular point, Proceedings of the international symposium on Symbolic and algebraic computation, p.231-235, August 20-24, 1990, Tokyo, Japan [doi>10.1145/96877.96934]
	7	V. Dietrich. Zur Reduktion von linearen Differentialgleichungssystemen. Math. Ann., 237:79--95, 1978.
	8	Mark Giesbrecht , Arne Storjohann, Computing rational forms of integer matrices, Journal of Symbolic Computation, v.34 n.3, p.157-172, September 2002 [doi>10.1006/jsco.2002.0554]
	9	A. Hilali and A. Wazner. Formes super-irr éductibles des systèmes diérentiels linéaires. Numer. Math., 50:429--449, 1987.
	10	Claude-Pierre Jeannerod, An algorithm for the eigenvalue perturbation problem: reduction of a κ-matrix to a Lidskii matrix, Proceedings of the 2000 international symposium on Symbolic and algebraic computation, p.184-191, July 2000, St. Andrews, Scotland [doi>10.1145/345542.345627]
	11	C.-P.Jeannerod. Formes normales de perturbations de matrices: étude et calcul exact. PhD thesis, Institut National Polytechnique de Grenoble, 2000.
	12	A. Levelt. Stabilizing Differential Operators: a method for Computing Invariants at Irregular Singularities. Differential Equations and Computer Algebra, M. Singer (ed.), pages 181--228, 1991.
	13	V. Lidskii. Perturbation theory of non-conjugate operators. U.S.S.R. Comput. Math. and Math. Phys., 1:73--85, 1965.
	14	J. Moser. The order of a singularity in Fuchs' theory. Math. Z., pages 379--398, 1960.
	15	E. Pflügel. Réesolution symbolique des systèmes differentiels linéaires. PhD thesis, LMC-IMAG, 1998.
	16	E. Pflügel. Effective formal reduction of linear differential systems. Appl.Alg.Eng. Comm. Comp., 10(2):153--187, 2000.
	17	H. Turritin. Convergent solutions of ordinary linear homogeneous differential equations in the neighborhood of an irregular singular point. Acta Math., 93:27--66, 1955.
	18	W. Wasow. Asymptotic Expansions for Ordinary Differential Equations. Robert E. Krieger Publishing, 1967.

CITED BY 3

	Eckhard Pflüegel, A rational decomposition-lemma for systems of linear differential-algebraic equations, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, July 20-23, 2008, Linz/Hagenberg, Austria
	Moulay A. Barkatou , Eckhard Pflügel, On the Moser- and super-reduction algorithms of systems of linear differential equations and their complexity, Journal of Symbolic Computation, v.44 n.8, p.1017-1036, August, 2009
	Moulay A. Barkatou , Gary Broughton , Eckhard Pflügel, Regular systems of linear functional equations and applications, Proceedings of the twenty-first international symposium on Symbolic and algebraic computation, July 20-23, 2008, Linz/Hagenberg, Austria