1,721,980 research outputs found
B-spline collocation discretizations of caputo and Riemann-Liouville derivatives: A matrix comparison
No full textTwo of the most famous definitions of fractional derivatives are the Riemann-Liouville and the Caputo ones. In principle, these formulations are not equivalent and ask for different levels of regularity of the considered function. By focusing on a B-spline collocation discretization of both kind of derivatives, we show that when the fractional order α ranges in (1, 2) their difference in terms of matrices corresponds to a rank-1 correction whose spectral norm increases with the mesh-size n and is o(n). On one hand, this implies that the spectral distribution for the B-spline collocation matrices corresponding to the Riemann-Liouville and Caputo derivatives coincide; on the other hand, the presence of the rank-1 correction makes the Caputo matrices worse conditioned for α tending to 1 due to a larger maximum singular value. Some linear algebra consequences of all this knowledge are discussed, and a selection of numerical experiments that validate our findings is provided
Introduzione all'inventario identificativo del patrimonio museale: TOMUS, modello di rilevamento
No full textIl progetto TOMUS, promosso in collaborazione con la Regione Toscana, ha inteso proporre un modello di rilevamento in grado di creare un'anagrafe identificativa di tutti i musei regionali. Caratteristiche e morfologie diverse sono confluite in un'unica scheda consentendo ricerche a più livelli che evidenziano la ricchezza del patrimonio artistico presente in Toscana
The asymptotic spectrum of flipped multilevel Toeplitz matrices and of certain preconditionings
Full text linkIn this work, we perform a spectral analysis of flipped multilevel Toeplitz sequences, i.e., we study the asymptotic spectral behavior of , where is a real, square multilevel Toeplitz matrix generated by a function and is the exchange matrix, which has 1's on the main antidiagonal. In line with what we have shown for unilevel flipped Toeplitz matrix sequences, the asymptotic spectrum is determined by a 2 x 2 matrix-valued function whose eigenvalues are . Furthermore, we characterize the eigenvalue distribution of certain preconditioned flipped multilevel Toeplitz sequences with an analysis that covers both multilevel Toeplitz and circulant preconditioners. Finally, all our findings are illustrated by several numerical experiments
Spectral properties of flipped Toeplitz matrices and related preconditioning
Full text linkIn this work, we investigate the spectra of "flipped" Toeplitz sequences, i.e., the asymptotic spectral behaviour of {YnTn(f)}n, where Tn(f)∈Rn×n is a real Toeplitz matrix generated by a function f∈L1([-π,π]), and Yn is the exchange matrix, with 1s on the main anti-diagonal. We show that the eigenvalues of YnTn(f) are asymptotically described by a 2×2 matrix-valued function, whose eigenvalue functions are ±|f|. It turns out that roughly half of the eigenvalues of YnTn(f) are well approximated by a uniform sampling of |f| over [-π,π] while the remaining are well approximated by a uniform sampling of -|f| over the same interval. When f vanishes only on a set of measure zero, this motivates that the spectrum is virtually half positive and half negative. Some insights on the spectral distribution of related preconditioned sequences are provided as well. Finally, a wide number of numerical results illustrate our theoretical findings
Cognizione sociale e autismo. Modelli comportamentali, implicazioni cliniche e valutazione
No full textTaxonomy and Phyllomorphogenesis of the Carnian/Norian conodonts from Pizzo Mondello section (Sicani Mountains, Sicily)
No full text
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
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