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pro vyhledávání: '"Sommariva A"'
We make a further step in the unisolvence open problem for unsymmetric Kansa collocation, proving nonsingularity of Kansa matrices with polyharmonic splines and random fictitious centers, for second-order elliptic equations with mixed boundary condit
Externí odkaz:
http://arxiv.org/abs/2410.03279
Autor:
Sommariva, Alvise, Vianello, Marco
We give a short proof of almost sure invertibility of unsymmetric random Kansa collocation matrices by a class of analytic RBF vanishing at infinity, for the Poisson equation with Dirichlet boundary conditions. Such a class includes popular Positive
Externí odkaz:
http://arxiv.org/abs/2405.18550
Autor:
Sommariva, A., Vianello, M.
We prove that interpolation matrices for Generalized MultiQuadrics (GMQ) of order greater than one are almost surely nonsingular without polynomial addition, in any dimension and with any continuous random distribution of sampling points. We also inc
Externí odkaz:
http://arxiv.org/abs/2404.10117
Autor:
Decker, J., Hoppe, M., Sheikh, U., Duval, B. P., Papp, G., Simons, L., Wijkamp, T., Cazabonne, J., Coda, S., Devlaminck, E., Ficker, O., Hellinga, R., Kumar, U., Savoye-Peysson, Y., Porte, L., Reux, C., Sommariva, C., Biwolé, A. Tema, Vincent, B., Votta, L., Team, the TCV, Team, the EUROfusion Tokamak Exploitation
Runaway electrons (REs) are a concern for tokamak fusion reactors from discharge startup to termination. A sudden localized loss of a multi-megaampere RE beam can inflict severe damage to the first wall. Should a disruption occur, the existence of a
Externí odkaz:
http://arxiv.org/abs/2404.09900
Unisolvence of unsymmetric Kansa collocation is still a substantially open problem. We prove that Kansa matrices with MultiQuadrics and Inverse MultiQuadrics for the Dirichlet problem of the Poisson equation are almost surely nonsingular, when the co
Externí odkaz:
http://arxiv.org/abs/2403.18017
Existence of sufficient conditions for unisolvence of Kansa unsymmetric collocation for PDEs is still an open problem. In this paper we make a first step in this direction, proving that unsymmetric collocation matrices with Thin-Plate Splines for the
Externí odkaz:
http://arxiv.org/abs/2403.06646
Autor:
Sommariva, Alvise
The purpose of this work is to introduce a strategy for determining the nodes and weights of a low-cardinality positive cubature formula nearly exact for polynomials of a given degree over spherical polygons. In the numerical section we report the re
Externí odkaz:
http://arxiv.org/abs/2403.05733
Autor:
Sommariva, Alvise, Vianello, Marco
In a recent paper almost sure unisolvence of RBF interpolation at random points with no polynomial addition was proved, for Thin-Plate Splines and Radial Powers with noninteger exponent. The proving technique left unsolved the case of odd exponents.
Externí odkaz:
http://arxiv.org/abs/2401.13322
In this note we prove almost sure unisolvence of RBF interpolation on randomly distributed sequences by a wide class of polyharmonic splines (including Thin-Plate Splines), without polynomial addition.
Externí odkaz:
http://arxiv.org/abs/2312.13710
We construct admissible polynomial meshes on piecewise polynomial or trigonometric curves of the complex plane, by mapping univariate Chebyshev points. Such meshes can be used for polynomial least-squares, for the extraction of Fekete-like and Leja-l
Externí odkaz:
http://arxiv.org/abs/2311.06511