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The Convergence of Least-Squares Progressive Iterative Approximation with Singular Iterative Matrix

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arxiv 1707.09109 v1 pith:4IJT3DXR submitted 2017-07-28 cs.NA cs.NA

Hongwei Lin , Qi Cao , Xiaoting Zhang This is my paper · ORCID
classification cs.NA
keywords iterativeleast-squareslspiamatrixapproximationconvergentdengprogressive
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    math.NA 2019-08 conditional novelty 6.0 of 10

    A new 'with memory' variant of the LSPIA method accelerates least-squares B-spline curve and surface fitting by reusing previous iterates, with a proven faster convergence rate for totally positive bases.

  2. Implicit Progressive-Iterative Approximation for Curve and Surface Reconstruction

    math.NA 2019-09 conditional novelty 5.0 of 10

    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.

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