76 citations · 129 across the 8 of their papers we have counts for
9 papers
Multiple zeros of nonlinear systems
Barry H. Dayton, Tien-Yien Li, Zhonggang Zeng
As an attempt to bridge between numerical analysis and algebraic geometry, this paper formulates the multiplicity for the general nonlinear system at an isolated zero, presents an…
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…
The numerical greatest common divisor of univariate polynomials
Zhonggang Zeng
This paper presents a regularization theory for numerical computation of polynomial greatest common divisors and a convergence analysis, along with a detailed description of a blac…
Sensitivity and computation of a defective eigenvalue
Zhonggang Zeng
A defective eigenvalue is well documented to be hypersensitive to data perturbations and round-off? errors, making it a formidable challenge in numerical computation particularly w…
A numerical method for computing the Jordan Canonical Form
Zhonggang Zeng, Tien-Yien Li
The Jordan Canonical Form of a matrix is highly sensitive to perturbations, and its numerical computation remains a formidable challenge. This paper presents a regularization theor…
On the sensitivity of singular and ill-Conditioned linear systems
Zhonggang Zeng
Solving a singular linear system for an individual vector solution is an ill-posed problem with a condition number infinity. From an alternative perspective, however, the general s…
Singular algebraic equations with empirical data
Zhonggang Zeng
Singular equations with rank-deficient Jacobians arise frequently in algebraic computing applications. As shown in case studies in this paper, direct and intuitive modeling of alge…
Geometric modeling and regularization of algebraic problems
Zhonggang Zeng
Discontinuity with respect to data perturbations is common in algebraic computation where solutions are often highly sensitive. Such problems can be modeled as solving systems of e…
A Newton's Iteration Converges Quadratically to Nonisolated Solutions Too
Zhonggang Zeng
The textbook Newton's iteration is practically inapplicable on solutions of nonlinear systems with singular Jacobians. By a simple modification, a novel extension of Newton's itera…