Order stars is a recently developed technique to analyze and
explain the behaviour of numerical methods. The main idea is to
explore different features of numerical algorithms as properties of
analytical functions in various portions of the complex plane.
Thus, for example, the order of some numerical methods for ordinary
differential equations can be translated to the language of
approximation theory - specifically, to the question of how well a
given rational function R approximates the exponential. Likewise,
stability properties of the underlying method can be expressed as
some other features of the function R. In this formulation, order
stars establish the relationship between order and stability,
helping in the search for better and more efficient computational
algorithms.
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