An iterative implicit B-spline fitting method, I-PIA, converges to the minimum-norm least-squares fit and empirically reconstructs curves and surfaces without spurious sheets.
The Convergence of Least-Squares Progressive Iterative Approximation with Singular Iterative Matrix
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abstract
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.
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Implicit Progressive-Iterative Approximation for Curve and Surface Reconstruction
An iterative implicit B-spline fitting method, I-PIA, converges to the minimum-norm least-squares fit and empirically reconstructs curves and surfaces without spurious sheets.