260 research outputs found
On the accuracy of solving confluent Prony systems
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, such as
frequency estimation and nonlinear Fourier inversion. 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" behavior 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.
Numerical tests suggest that "global" solution techniques such as Prony's
algorithm and ESPRIT method are suboptimal when compared to this theoretical
"best local" behavior
Decimated generalized Prony systems
We continue studying robustness of solving algebraic systems of Prony type
(also known as the exponential fitting systems), which appear prominently in
many areas of mathematics, in particular modern "sub-Nyquist" sampling
theories. We show that by considering these systems at arithmetic progressions
(or "decimating" them), one can achieve better performance in the presence of
noise. We also show that the corresponding lower bounds are closely related to
well-known estimates, obtained for similar problems but in different contexts
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