Symbolic computation of normal forms for semi-simple cases
نویسندگان
چکیده
منابع مشابه
Symbolic computation of normal forms for semi-simple cases
This paper presents a method and computer programs for computing the normal forms of ordinary di erential equations whose Jacobian matrix evaluated at an equilibrium involves semi-simple eigenvalues. The method can be used to deal with systems which are not necessarily described on a center manifold. An iterative procedure is developed for nding the closed-form expressions of the normal forms a...
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Abstract. In this paper we present a simple and efficient method for computing center manifold and normal forms of differential equations. The main attention is focused on general semi-simple singularities, that is, the Jacobian of a given system evaluated at an equilibrium contains semi-simple eigenvalues. The method combines the computation of center manifold and normal form in one unified pr...
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Following the results of cite{Med}, regarding the Aluthge transform of polynomial matrices, the symbolic computation of the Duggal transform of a polynomial matrix $A$ is developed in this paper, using the polar decomposition and the singular value decomposition of $A$. Thereat, the polynomial singular value decomposition method is utilized, which is an iterative algorithm with numerical charac...
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ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1999
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(98)00222-2