Rational multiple criterion approximation and rational complex approximation by differential correction-type algorithms

This work shows how to extend the differential correction algorithm (a well-known technique for rational minimax approximation of real functions) to handle simultaneous minimax approximation of magnitude and phase of complex-valued functions defined on the unit circle of the complex plane. The propo...

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Bibliographic Details
Published in:SIAM journal on scientific computing 1995-07, Vol.16 (4), p.974-991
Main Authors: CORTELAZZO, G, MIAN, G. A, MORANDINI, M
Format: Article
Language:English
Subjects:
Algorithms
Approximation
Approximations and expansions
Calculus of variations and optimal control
Design specifications
Exact sciences and technology
Mathematical analysis
Mathematics
Optimization
Sciences and techniques of general use
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Summary:This work shows how to extend the differential correction algorithm (a well-known technique for rational minimax approximation of real functions) to handle simultaneous minimax approximation of magnitude and phase of complex-valued functions defined on the unit circle of the complex plane. The proposed procedure enjoys global convergence to local best approximants with poles only inside the unit circle. Hence, the approximants obtained can be used as transfer functions of causal and stable linear systems, and the proposed technique can be profitably applied to digital filter design. The differential correction strategy can also be applied to rational complex approximation, and can also be extended to the case of multidimensional rational functions, retaining the properties of the one-dimensional case. This ability to produce stable transfer functions is of special interest in the multidimensional case.
ISSN:1064-8275
1095-7197
DOI:10.1137/0916057