On the accuracy of solving confluent Prony systems

Details On the accuracy of solving confluent Prony systems On the accuracy of solving confluent Prony systems

2011-06-06

arxiv.org/abs/1106.1137v1

Mathematics

Classical Analysis and ODEs

Scientific paper

In this paper we consider several nonlinear systems of algebraic equations which can be called "Prony-type". These systems arise in various reconstruction problems in several branches of theoretical and applied mathematics. Usually, the underlying models exhibit some kind of discontinuities, and the said systems happen to capture their discontinuous nature in geometric terms. Consequently, the question of stability of solution with respect to errors in the right-hand side becomes critical for the success of any particular application. We investigate the question of "maximal possible accuracy" of solving Prony-type systems, putting stress on the "local" behaviour which approximates situations with low absolute measurement error. The accuracy estimates are formulated in very simple geometric terms, shedding some light on the structure of the problem. A comparison with recurrence-based "global" solution method is also provided.

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