arXiv subjects

Zhenyi Ji

Publications and source records attributed to Zhenyi Ji.

2 recordsLinked to original sources

arXiv2013

Numerical method for real root isolation of semi-algebraic system and its applications

In this paper, based on the homotopy continuation method and the interval Newton method, an efficient algorithm is introduced to isolate the real roots of semi-algebraic system. Tests on some random examples and a variety of problems including transcendental functions arising in many applications show that the new algorithm reduces the cost substantially compared with the traditional symbolic approaches.

math.NA↗

arXiv2010

An improvement upon unmixed decomposition of an algebraic variety

Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and developed efficient algorithms using $Gr$ö$bner$ basis method. In this paper, we try to modify the computation of unmixed decomposition of an algebraic variety based on improving the computation of $Zero(sat(\mathbb{T}))$, where $\mathbb{T}$ is a triangular set in $\textbf{K[X]}$.

math.AC↗