arXiv subjects

Zheng-Da Huang

Publications and source records attributed to Zheng-Da Huang.

2 recordsLinked to original sources

arXiv2022

A class of inexact block factorization preconditioners for indefinite matrices with a three-by-three block structure

We consider using the preconditioned-Krylov subspace method to solve the system of linear equations with a three-by-three block structure. By making use of the three-by-three block structure, eight inexact block factorization preconditioners, which can be put into a same theoretical analysis frame, are proposed based on a kind of inexact factorization. By generalizing Bendixson Theorem and developing a unified technique of spectral equivalence, the bounds of the real and imaginary parts of eigenvalues of the preconditioned matrices are obtained. The comparison to eleven existed exact and inexact preconditioners shows that three of the proposed preconditioners can lead to high-speed and effective preconditioned-GMRES in most tests.

math.NA↗

arXiv2019

On a progressive and iterative approximation method with memory for least square fitting

In this paper, we present a progressive and iterative approximation method with memory for least square fitting(MLSPIA). It adjusts the control points and the weighted sums iteratively to construct a series of fitting curves (surfaces) with three weights. For any normalized totally positive basis even when the collocation matrix is of deficient column rank, we obtain a condition to guarantee that these curves (surfaces) converge to the least square fitting curve (surface) to the given data points. It is proved that the theoretical convergence rate of the method is faster than the one of the progressive and iterative approximation method for least square fitting (LSPIA) in [Deng C-Y, Lin H-W. Progressive and iterative approximation for least squares B-spline curve and surface fitting. Computer-Aided Design 2014;47:32-44] under the same assumption. Examples verify this phenomenon.

math.NA↗