排序方式: 共有22条查询结果,搜索用时 19 毫秒
1.
We prove that the resultant of two “sufficiently generic” bivariate polynomials over a finite field can be computed in quasi-linear expected time, using a randomized algorithm of Las Vegas type. A similar complexity bound is proved for the computation of the lexicographical Gröbner basis for the ideal generated by the two polynomials. 相似文献
2.
Yi Li 《Applied mathematics and computation》2009,215(7):2495-2501
A hybrid algorithm for computing the determinant of a matrix whose entries are polynomials is presented. It is based on the dimension-decreasing algorithm [22] and the parallel algorithm for computing a symbolic determinant of [19]. First, through the dimension-decreasing algorithm, a given multivariate matrix can be converted to a bivariate matrix. Then, the parallel algorithm can be applied to effectively compute the determinant of the bivariate matrix. Experimental results show that the new algorithm can not only reduce enormously the intermediate expression swell in the process of symbolic computation, but also achieve higher degree of parallelism, compared with the single parallel algorithm given in [19]. 相似文献
3.
An ODE model for oncolytic virus dynamics with four parameters is discussed. Although it is hard to obtain the explicit expressions of coordinates of equilibria, we find distribution of equilibria qualitatively, and obtain the exact number of equilibria and their qualitative properties. We further give a complete analysis on local bifurcations such as saddle–node, Bogdanov–Takens, and Hopf bifurcations. Resultant elimination is applied to decompose the semi-algebraic varieties of Lyapunov quantities under the restriction of biological meaning, and we show that the weak focus is of order at most 3. 相似文献
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本文主要讨论交换环上多项式结式的一些性质.首先,我们证明了交换环上一种乘积的结式等于结式的乘积的性质,然后,我们证明了交换环上一种和的结式具有的性质,并且给出了交换环上结式为零的一个充分条件. 相似文献
5.
The E-characteristic polynomial of an even order supersymmetric tensor is a useful tool in determining the positive definiteness of an even degree multivariate form. In this paper, for an even order tensor, we first establish the formula of its E-characteristic polynomial by using the classical Macaulay formula of resultants, then give an upper bound for the degree of that E-characteristic polynomial. Examples illustrate that this bound is attainable in some low order and dimensional cases. 相似文献
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Guo-Jin Wang & T. W. Sederberg 《计算数学(英文版)》1999,17(1):33-40
This is a continuation of short communication$^{[1]}$. In [1] a verification of the
implicitization equation for degree two rational Bézier curves is presented which
does not require the use of resultants. This paper presents these verifications in the general cases, i.e., for degree $n$ rational Bézier curves. Thus some interesting interplay between the structure of the $n×n$ implicitization matrix and the de Casteljau algorithm is revealed. 相似文献
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Costanza Conti Luca Gemignani Lucia Romani 《Linear algebra and its applications》2009,431(10):1971-1987
In this paper we present a general strategy to deduce a family of interpolatory masks from a symmetric Hurwitz non-interpolatory one. This brings back to a polynomial equation involving the symbol of the non-interpolatory scheme we start with. The solution of the polynomial equation here proposed, tailored for symmetric Hurwitz subdivision symbols, leads to an efficient procedure for the computation of the coefficients of the corresponding family of interpolatory masks. Several examples of interpolatory masks associated with classical approximating masks are given. 相似文献
10.
We give an efficient algorithm for solving resultant form equations over number fields. This is the first time that such equations are completely solved by reducing them to unit equations in two variables.