Generalized Subresultants for Computing the Smith Normal Form of Polynomial Matrices
نویسندگان
چکیده
منابع مشابه
Smith Normal Form and acyclic matrices
An approach, based on the Smith Normal Form, is introduced to study the spectra of symmetric matrices with a given graph. The approach serves well to explain how the path cover number (resp. diameter of a tree T ) is related to the maximal multiplicity MaxMult(T ) occurring for an eigenvalue of a symmetric matrix whose graph is T (resp. the minimal number q(T ) of distinct eigenvalues over the ...
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A Las Vegas probabilistic algorithm is presented that finds the Smith normal form S ∈ Q[x] of a nonsingular input matrix A ∈ Z [x]. The algorithm requires an expected number of O (̃nd(d + n log ||A||)) bit operations (where ||A|| bounds the magnitude of all integer coefficients appearing in A and d bounds the degrees of entries of A). In practice, the main cost of the computation is obtaining a ...
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Smith normal form computation has many applications in group theory, module theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Smith normal form of large dense matrices. The computation has two main problems: the high execution time and the memory requirements, ...
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Smith normal form computation has many applications in group theory, module theory and number theory. As the entries of the matrix and of its corresponding transformation matrices can explode during the computation, it is a very difficult problem to compute the Smith normal form of large dense matrices. The computation has two main problems: the high execution time and the memory requirements, ...
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ژورنال
عنوان ژورنال: Journal of Symbolic Computation
سال: 1995
ISSN: 0747-7171
DOI: 10.1006/jsco.1995.1050