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Biorthogonal system

About: Biorthogonal system is a research topic. Over the lifetime, 2190 publications have been published within this topic receiving 32209 citations.


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TL;DR: In this paper, the authors obtained Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces, and showed that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces.
Abstract: We obtain Lebesgue-type inequalities for the greedy algorithm for arbitrary complete seminormalized biorthogonal systems in Banach spaces. The bounds are given only in terms of the upper democracy functions of the basis and its dual. We also show that these estimates are equivalent to embeddings between the given Banach space and certain discrete weighted Lorentz spaces. Finally, the asymptotic optimality of these inequalities is illustrated in various examples of not necessarily quasi-greedy bases.

20 citations

Journal ArticleDOI
TL;DR: In this article, the biorthogonal decomposition analysis of signals from an array of Mirnov coils is able to provide the spatial structure and the temporal evolution of magnetohydrodynamic (MHD) instabilities in a tokamak.
Abstract: The biorthogonal decomposition analysis of signals from an array of Mirnov coils is able to provide the spatial structure and the temporal evolution of magnetohydrodynamic (MHD) instabilities in a tokamak. Such analysis can be adapted to a data acquisition and elaboration system suitable for fast real time applications such as instability detection and disruption precursory markers computation. This paper deals with the description of this technique as applied to the Frascati Tokamak Upgrade (FTU).

20 citations

Journal ArticleDOI
TL;DR: In this paper, a new analytical set of complete and biorthogonal potential-density basis functions for soft-centred stellar systems has been proposed, which are intrinsically suitable for modeling three dimensional, soft-centered stellar systems and complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao.
Abstract: We use the weighted integral form of spherical Bessel functions, and introduce a new analytical set of complete and biorthogonal potential–density basis functions. The potential and density functions of the new set have finite central values and they fall off, respectively, similar to r (1+l) and r (4+l) at large radii where l is the latitudinal quantum number of spherical harmonics. The lowest order term associated with l = 0 is the perfect sphere of de Zeeuw. Our basis functions are intrinsically suitable for the modeling of three dimensional, soft-centred stellar systems and they complement the basis sets of Clutton-Brock, Hernquist & Ostriker and Zhao. We test the performance of our functions by expanding the density and potential profiles of some spherical and oblate galaxy models.

20 citations

Journal ArticleDOI
TL;DR: This paper proposes the use of wavelets for the identification of an unknown sparse system whose impulse response (IR) is rich in spectral content and uses biorthogonal wavelets which fulfil both of these two requirements to provide additional gain in performance.
Abstract: This paper proposes the use of wavelets for the identification of an unknown sparse system whose impulse response (IR) is rich in spectral content. The superior time localization property of wavelets allows for the identification and subsequent adaptation of only the nonzero IR regions, resulting in lower complexity and faster convergence speed. An added advantage of using wavelets is their ability to partially decorrelate the input, thereby further increasing convergence speed. Good time localization of nonzero IR regions requires high temporal resolution while good decorrelation of the input requires high spectral resolution. To this end we also propose the use of biorthogonal wavelets which fulfil both of these two requirements to provide additional gain in performance. The paper begins with the development of the wavelet-basis (WB) algorithm for sparse system identification. The WB algorithm uses the wavelet decomposition at a single scale to identify the nonzero IR regions and subsequently determines the wavelet coefficients of the unknown sparse system at other scale levels that require adaptation as well. A special implementation of the WB algorithm, the successive-selection wavelet-basis (SSWB), is then introduced to further improve performance when certain a priori knowledge of the sparse IR is available. The superior performance of the proposed methods is corroborated through simulations.

20 citations

Journal ArticleDOI
TL;DR: A strengthened Cauchy-Schwarz inequality for spaces of biorthogonal wavelets defined on the real line and on the interval is proved in this paper, which is a fundamental tool in the analysis of the multilevel methods and plays an important role in the a posteriori error estimates for hierarchical methods.
Abstract: A strengthened Cauchy–Schwarz inequality for spaces of biorthogonal wavelets defined on the real line and on the interval is proved. The strengthened Cauchy–Schwarz inequality is a fundamental tool in the analysis of the multilevel methods and, in particular, plays an important role in the a posteriori error estimates for hierarchical methods. Mathematics subject classification (1991): 42C99.

20 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20241
202329
2022105
202155
202058
201960