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Computational methods for modelling of nonlinear systems
Preface Contents 1 Overview I Methods of Operator Approximation in System Modelling 2 Nonlinear Operator Approximation with Preassigned Accuracy 2.1 Introduction 2.2 Generic formulation of theExpand
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Optimal multilinear estimation of a random vector under constraints of causality and limited memory
TLDR
A new technique is provided for random vector estimation from noisy data under the constraints that the estimator is causal and dependent on at most a finite number p of observations. Expand
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Optimal fixed rank transform of the second degree
We present a new technique with potential applications to numerous areas in signal processing including data compression, filtering, blind channel equalization, and feature selection andExpand
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An optimal filter of the second order
TLDR
We present a new technique allowing us to find an optimal filter in the class of so-called second-order filters that generalizes and improves an optimal linear filter associated with the concept of Wiener filtering. Expand
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Computational Methods for Modeling of Nonlinear Systems
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Method of recurrent best estimators of second degree for optimal filtering of random signals
TLDR
A new approach to random signal filtering from observed data is proposed. Expand
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Optimal transform formed by a combination of nonlinear operators: the case of data dimensionality reduction
TLDR
In this paper, a new approach to constructing optimal nonlinear transforms of random vectors is proposed and justified. Expand
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On the constructive approximation of non-linear operators in the modelling of dynamical systems
TLDR
In this paper we propose a systematic theoretical procedure for the constructive approximation of non-linear operators and show how this procedure can be applied to the modelling of dynamical systems. Expand
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A methodology for the constructive approximation of nonlinear operators defined on noncompact sets
We consider the constructive approximation of a non-linear operator that is known on a bounded but not necessarily compact set. Our main result can be regarded as an extension of the classicalExpand
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