Topics in matrix analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Progressive iterative approximation and bases with the fastest convergence rates
Computer Aided Geometric Design
Interpolation by geometric algorithm
Computer-Aided Design
Totally positive bases and progressive iteration approximation
Computers & Mathematics with Applications
Local progressive-iterative approximation format for blending curves and patches
Computer Aided Geometric Design
The convergence of the geometric interpolation algorithm
Computer-Aided Design
A comparison of different progressive iteration approximation methods
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
Computer Graphics in China: Convergence analysis for B-spline geometric interpolation
Computers and Graphics
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Two recent tools for constructing interpolating curves and surfaces are the progressive iteration approximation (PIA) and the geometric algorithm. This communication has two main goals. On the one hand, we show that the proof of Theorem 1 of [5] on the convergence of the geometric algorithm is not correct. On the other hand, we clarify the difference between several variants of the PIA iterations by introducing the idea of preconditioned PIA iterations.