GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems
SIAM Journal on Scientific and Statistical Computing
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
Totally positive bases and progressive iteration approximation
Computers & Mathematics with Applications
Weighted progressive iteration approximation and convergence analysis
Computer Aided Geometric Design
Local progressive-iterative approximation format for blending curves and patches
Computer Aided Geometric Design
A comparison of different progressive iteration approximation methods
MMCS'08 Proceedings of the 7th international conference on Mathematical Methods for Curves and Surfaces
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This note revisits the progressive iteration approximation property and some recent modifications from the point of view of iterative methods for solving linear systems. In particular we show the connection with the classical Richardson iteration and modified Richardson iteration. We propose to use GMRES as an alternative iterative method. Numerical experiments achieve much better approximations with only few iterations, which can be explained by an interpretation of the GMRES method.