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Approximation theory for matrices [PDF]
Nuclear Physics B - Proceedings Supplements, 2004 We review the theory of optimal polynomial and rational Chebyshev approximations, and Zolotarev's formula for the sign function over the range ( \leq |z| \leq1). We explain how rational approximations can be applied to large sparse matrices efficiently by making use of partial fraction expansions and multi-shift Krylov space solvers.
A.D. Kennedy +25 more
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A sufficient condition for null controllability of nonlinear control systems [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2009 Classical control methods such as Pontryagin Maximum Principle and Bang-Bang Principle and other methods are not usually useful for solving opti-mal control systems (OCS) specially optimal control of nonlinear systems (OCNS).
A. Heydari, A.V. Kamyad
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Higher ideal approximation theory [PDF]
Transactions of the American Mathematical Society, 2022 Our aim in this paper is to introduce the so-called ideal approximation theory into higher homological algebra. To this end, we introduce some important notions from approximation theory into the theory of n n -exact categories and prove some results.
Asadollahi, Javad, Sadeghi, Somayeh
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Generalised discretisation of continuous-time distributions
The Journal of Engineering, 2020 In this study, the definition of discretisation that was proposed recently for continuous-time distributions is made applicable not only to ordinary functions but to a variety of distributions including weak derivatives such that they could be viewed ...
Shin Kawai, Noriyuki Hori, Noriyuki Hori
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IET Radar, Sonar & Navigation, 2021 Adaptive beamformers at the element level usually require a great number of training samples and the computational cost for calculating the weight vector for large phased array antennas is very high, which make it difficult for real‐time applications. To
Wei Gao +4 more
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On boundedness inequalities in the variation of certain Schurer-type operators; pp. 1–9 [PDF]
Proceedings of the Estonian Academy of Sciences, 2016 This paper is concerned with boundedness inequalities in the variation for the higher order derivatives of general Schurertype operators. In particular, the boundedness inequalities in the variation for the higher order derivatives of the Bernsteinâ ...
Andi Kivinukk, Tarmo Metsmägi
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Approximation Theory and Related Applications
Axioms, 2022 The theory of approximation of functions is one of the central branches of mathematical analysis [...]
Yurii Kharkevych
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Data Based Construction of Kernels for Semi-Supervised Learning With Less Labels
Frontiers in Applied Mathematics and Statistics, 2019 This paper deals with the problem of semi-supervised learning using a small number of training samples. Traditional kernel based methods utilize either a fixed kernel or a combination of judiciously chosen kernels from a fixed dictionary. In contrast, we
Hrushikesh Mhaskar +3 more
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Algorithms and error bounds for multivariate piecewise constant approximation [PDF]
, 2010 We review the surprisingly rich theory of approximation of functions of many vari- ables by piecewise constants. This covers for example the Sobolev-Poincar´e inequalities, parts of the theory of nonlinear approximation, Haar wavelets and tree ...
Davydov, Oleg
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Beam-space direct localisation using passive arrays with random shape errors
The Journal of Engineering, 2019 Passive localisation with high accuracy is attractive in numerous fields. Beam-space direct position determination (BS-DPD) using antenna arrays is a promising positioning method which possesses both excellent performance and moderate complexity ...
Ning Zhang +3 more
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