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This paper presents a modified Thiele-Werner algorithm to construct a kind of reliable vector-valued rational interpolants (RVRIs) and then studies their existence. The reliability of this method means that if a solution of the basic vector-valued rational interpolation problem exists, the method given in this paper finds it. Then a method for testing the existence for RVRIs and some methods for dealing with unattainable points for RVRIs are given. [ABSTRACT FROM AUTHOR]

In this paper, we describe a variant of a solution for a common problem in applied statistics—we offer a variant method for estimating the parameters of a dynamic system, and observe its magnitudes, which statistically depend on the sequence of states of the system that are not observed. The method is realized by means of the multipolynomial approximations algorithm (the MPA algorithm). The method is validated by applying it to a problem of correction of finite sets of nominal experimental data on which nominal functions are constructed equationsby means of interpolation from the current states of the system. Nominal experimental data are presented on a finite set of points covering the domains of definition of the nominal functions. The nominal equations of motion of the dynamical system are defined by the nominal functions. In this paper, the concrete example of the nominal equations of motion correspond to the longitudinal motion of the aircraft similar of the F-l6 aircraft. The nominal functions are the calculated aerodynamic characteristics. The nominal experimental data are recorded by means of experiments in a wind-tunnel. The outcomes of measurements of the parameters of motion of the aircraft act on inputs for the MPA algorithm on a segment of real flight. The MPA algorithm defines a 32×1-vector of estimates of parameters, which are additive corrections to the nominal experimental data. [ABSTRACT FROM AUTHOR]

Matching pursuit is an iterative method whereby a signal is decomposed into a linear combination of functions that are selected from a redundant dictionary. In the original paper by Mallat and Zhang, a dictionary of Gabor functions is proposed. Each Gabor function is the product of a Gaussian function with a complex sinusoid, and is specified by time, frequency and scale. Since these functions are qualitatively and quantitatively very similar to ultrasonic echoes, it is appropriate to use the matching pursuit method to decompose ultrasonic signals to locate and identify discrete echoes embedded in complex signals. In this paper, a modified implementation of the matching pursuit algorithm is described, where the algorithm is specifically designed for an efficient decomposition of ultrasonic signals. The size of the wavelet dictionary is adaptively determined by the spectrum of the ultrasonic signal and is further controlled by additional physically meaningful restrictions. In each iterative step, the pursuit of the matching function begins with a coarse grid in the parameter space of the dictionary, and the highest energy matching function is found by interpolation of this coarse grid over the parameters. The algorithm is applied to a variety of measured ultrasonic signals. Signals consisting of multiple echoes are successfully decomposed, and the individual wavelets are well-matched to the original echoes. © 2007 American Institute of Physics [ABSTRACT FROM AUTHOR]