8 citations · 16 across the 16 of their papers we have counts for
16 papers
Structural Analysis by Modified Signature Matrix for Integro-differential-algebraic Equations
Wenqiang Yang, Wenyuan Wu, Greg Reid
Integro-differential-algebraic equations (IDAE)s are widely used in applications of engineering and analysis. When there are hidden constraints in an IDAE, structural analysis is n…
Index Reduction for Degenerated Differential-Algebraic Equations by Embedding
Wenqiang Yang, Wenyuan Wu, Greg Reid
To find consistent initial data points for a system of differential-algebraic equations, requires the identification of its missing constraints. An efficient class of structural me…
Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations
Wenqiang Yang, Wenyuan Wu, Greg Reid
Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenab…
On the probability of generating a primitive matrix
Jingwei Chen, Yong Feng, Yang Liu +1
Given a integer primitive matrix (i.e., a matrix can be extended to an unimodular matrix over the integers) with the maximal absolute value of entr…
The numerical factorization of polynomials
Wenyuan Wu, Zhonggang Zeng
Polynomial factorization in conventional sense is an ill-posed problem due to its discontinuity with respect to coefficient perturbations, making it a challenge for numerical compu…
Visualizing Planar and Space Implicit Real Algebraic Curves with Singularities
Changbo Chen, Wenyuan Wu, Yong Feng
We present a new method for visualizing implicit real algebraic curves inside a bounding box in the -D or -D ambient space based on numerical continuation and critical point…
Optimal Solution of Linear Ordinary Differential Equations by Conjugate Gradient Method
Wenqiang Yang, Wenyuan Wu, Robert M. Corless
Solving initial value problems and boundary value problems of Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerica…
Error Estimation of Numerical Solvers for Linear Ordinary Differential Equations
Wenyuan Wu, Wenqiang Yang
Solving Linear Ordinary Differential Equations (ODEs) plays an important role in many applications. There are various numerical methods and solvers to obtain approximate solutions.…
The PSLQ Algorithm for Empirical Data
Yong Feng, Jingwei Chen, Wenyuan Wu
The celebrated integer relation finding algorithm PSLQ has been successfully used in many applications. PSLQ was only analyzed theoretically for exact input data, however, when the…
A Special Homotopy Continuation Method For A Class of Polynomial Systems
Yu Wang, Wenyuan Wu, Bican Xia
A special homotopy continuation method, as a combination of the polyhedral homotopy and the linear product homotopy, is proposed for computing all the isolated solutions to a speci…
Facial Reduction and SDP Methods for Systems of Polynomial Equations
Greg Reid, Fei Wang, Henry Wolkowicz +1
The real radical ideal of a system of polynomials with finitely many complex roots is generated by a system of real polynomials having only real roots and free of multiplicities. I…
Structural index reduction algorithms for differential algebraic equations via fixed-point iteration
Juan Tang, Wenyuan Wu, Xiaolin Qin +1
Motivated by Pryce's structural index reduction method for differential algebraic equations (DAEs), we show the complexity of the fixed-point iteration algorithm and propose a fixe…
Geometric involutive bases for positive dimensional polynomial ideals and SDP methods
Greg Reid, Fei Wang, Wenyuan Wu
Geometric involutive bases for polynomial systems of equations have their origin in the prolongation and projection methods of the geometers Cartan and Kuranishi for systems of PDE…
A Short Note on Zero-error Computation for Algebraic Numbers by IPSLQ
Yong Feng, Jingwei Chen, Wenyuan Wu
The PSLQ algorithm is one of the most popular algorithm for finding nontrivial integer relations for several real numbers. In the present work, we present an incremental version of…
Numerical method for real root isolation of semi-algebraic system and its applications
Zhenyi Ji, Wenyuan Wu, Yi Li +1
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. Te…
Real Root Isolation of Polynomial Equations Based on Hybrid Computation
Fei Shen, Wenyuan Wu, Bican Xia
A new algorithm for real root isolation of polynomial equations based on hybrid computation is presented in this paper. Firstly, the approximate (complex) zeros of the given polyno…