arXiv subjects

Jingwei Chen

Publications and source records attributed to Jingwei Chen.

21 records · Page 2Linked to original sources

arXiv2010

Parallel computation of real solving bivariate polynomial systems by zero-matching method

We present a new algorithm for solving the real roots of a bivariate polynomial system $Σ=\{f(x,y),g(x,y)\}$ with a finite number of solutions by using a zero-matching method. The method is based on a lower bound for bivariate polynomial system when the system is non-zero. Moreover, the multiplicities of the roots of $Σ=0$ can be obtained by a given neighborhood. From this approach, the parallelization of the method arises naturally. By using a multidimensional matching method this principle can be generalized to the multivariate equation systems.

cs.SC↗

arXiv2010

A complete algorithm to find exact minimal polynomial by approximations

We present a complete algorithm for finding an exact minimal polynomial from its approximate value by using an improved parameterized integer relation construction method. Our result is superior to the existence of error controlling on obtaining an exact rational number from its approximation. The algorithm is applicable for finding exact minimal polynomial of an algebraic number by its approximate root. This also enables us to provide an efficient method of converting the rational approximation representation to the minimal polynomial representation, and devise a simple algorithm to factor multivariate polynomials with rational coefficients. Compared with the subsistent methods, our method combines advantage of high efficiency in numerical computation, and exact, stable results in symbolic computation. we also discuss some applications to some transcendental numbers by approximations. Moreover, the Digits of our algorithm is far less than the LLL-lattice basis reduction technique in theory. In this paper, we completely implement how to obtain exact results by numerical approximate computations.

cs.SC↗

arXiv2009

Finding Exact Minimal Polynomial by Approximations

We present a new algorithm for reconstructing an exact algebraic number from its approximate value using an improved parameterized integer relation construction method. Our result is consistent with the existence of error controlling on obtaining an exact rational number from its approximation. The algorithm is applicable for finding exact minimal polynomial by its approximate root. This also enables us to provide an efficient method of converting the rational approximation representation to the minimal polynomial representation, and devise a simple algorithm to factor multivariate polynomials with rational coefficients. Compared with other methods, this method has the numerical computation advantage of high efficiency. The experimental results show that the method is more efficient than \emph{identify} in \emph{Maple} 11 for obtaining an exact algebraic number from its approximation. In this paper, we completely implement how to obtain exact results by numerical approximate computations.

cs.CC↗