2020/07/20 by Zhonggang Zeng
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Advanced Optimization Algorithms Research #Algebraic equation #Algebraic number #Algorithm #Applied mathematics #Computation #Computer science #Lipschitz continuity #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Matrix Theory and Algorithms #Nonlinear system #Regularization (linguistics) #Verifiable secret sharing #cs.NA #math.NA #msc:47J06 #msc:65F22 #msc:65J20
paper · pdf · doi:10.1145/3373207.3404066
openalex publication_date 2020/07/20 · arxiv created 2021/02/16 · arxiv updated 2021/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 equations at given data parameters. By appending auxiliary equations, the models can be formulated to satisfy four easily verifiable conditions so that the data form complex analytic manifolds on which the solutions maintain their structures and the Lipschitz continuity. When such a problem is given with empirical data, solving the system becomes a least squares problem whose solution uniquely exists and enjoys Lipschitz continuity as long as the data point is in a tubular neighborhood of the manifold. As a result, the singular problem is regularized as a well-posed computational problem.