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Complexity of factorization and GCD computation for linear ordinary differential operators

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Abstract

This paper presents an algorithm of polynomial complexity for finding greatest common (right) divisors of families of linear ordinary differential operators. An algorithm is presented for factorization of operators into the product of irreducible operators with complexity significantly better than that of previously known algorithms. Estimates are given for the coefficients of the expansion of the fundamental solution of the corresponding linear differential equation.

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Authors
  1. D. Yu. Grigor'ev
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 176, pp. 68–103, 1989.

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Grigor'ev, D.Y. Complexity of factorization and GCD computation for linear ordinary differential operators. J Math Sci 59, 823–841 (1992). https://doi.org/10.1007/BF01104106

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  • DOI: https://doi.org/10.1007/BF01104106

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