The Convergence of Least-Squares Progressive Iterative Approximation with Singular Iterative Matrix
For researchers using LSPIA in geometric modeling, this work removes a restrictive condition, ensuring broader applicability of the method.
This paper proves that the Least-Squares Progressive Iterative Approximation (LSPIA) method for B-spline fitting converges even when its iterative matrix is singular, extending previous convergence results that required nonsingularity.
Developed in [Deng and Lin, 2014], Least-Squares Progressive Iterative Approximation (LSPIA) is an efficient iterative method for solving B-spline curve and surface least-squares fitting systems. In [Deng and Lin 2014], it was shown that LSPIA is convergent when the iterative matrix is nonsingular. In this paper, we will show that LSPIA is still convergent even the iterative matrix is singular.