Synopsis
Unlock the math behind why the order of corrections shapes convergence in linear systems.
In this work, the author develops a general theory of ordering for linear successive iteration schemes. It explains how the way you sequence the correction steps can affect the error behavior and convergence of the method, across different grid structures and boundary conditions. The book also explores when different orderings share the same eigenvalues as the standard approach, and how to count and characterize those orderings for various problem sizes.
- How error matrices and their eigenvalues determine convergence rates.
- distinctions between the usual ordering and various ordered schemes.
- How the analysis extends to general n-order systems and different coupling patterns.
- Methods to enumerate and compare orderings that preserve eigenvalues.
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Ordering Properties of Linear Successive Iteration Schemes Classic Reprint
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