90 research outputs found
Image reconstruction from scattered Radon data by weighted positive definite kernel functions
We propose a novel kernel-based method for image reconstruction from scattered Radon data. To this end, we employ generalized Hermite–Birkhoff interpolation by positive definite kernel functions. For radial kernels, however, a straightforward application of the generalized Hermite–Birkhoff interpolation method fails to work, as we prove in this paper. To obtain a well-posed reconstruction scheme for scattered Radon data, we introduce a new class of weighted positive definite kernels, which are symmetric but not radially symmetric. By our construction, the resulting weighted kernels are combinations of radial positive definite kernels and positive weight functions. This yields very flexible image reconstruction methods, which work for arbitrary distributions of Radon lines. We develop suitable representations for the weighted basis functions and the symmetric positive definite kernel matrices that are resulting from the proposed reconstruction scheme. For the relevant special case, where Gaussian radial kernels are combined with Gaussian weights, explicit formulae for the weighted Gaussian basis functions and the kernel matrices are given. Supporting numerical examples are finally presented
Local RBF approximation for scattered data fitting with bivariate splines
In this paper we continue our earlier research [4] aimed at developing effcient methods of local approximation suitable for the first stage of a spline based two-stage scattered data fitting algorithm. As an improvement to the pure polynomial local approximation method used in [5], a hybrid polynomial/radial basis scheme was considered in [4], where the local knot locations for the RBF terms were selected using a greedy knot insertion algorithm. In this paper standard radial local approximations based on interpolation or least squares are considered and a faster procedure is used for knot selection, signicantly reducing the computational cost of the method. Error analysis of the method and numerical results illustrating its performance are given
Rendimento e qualidade fisiológica de sementes de duas variedades de azevém com diferentes manejos de adubação e cortes.
CONGREGA URCAMP 2012
Produção de sementes de genótipos de azevém (Lolium multiflorum L.) sob diferentes regimes de adubação nitrogenada e épocas de último corte.
Produção de forragem de genótipos de azevém (Lolium multiflorum L.) sob diferentes regimes de adubação nitrogenada.
Exact ground-state correlation functions of the one-dimensional strongly correlated electron models with the resonating-valence-bond ground state
We investigate the one-dimensional strongly correlated electron models which
have the resonating-valence-bond state as the exact ground state. The
correlation functions are evaluated exactly using the transfer matrix method
for the geometric representations of the valence-bond states. In this method,
we only treat matrices with small dimensions. This enables us to give
analytical results. It is shown that the correlation functions decay
exponentially with distance. The result suggests that there is a finite
excitation gap, and that the ground state is insulating. Since the
corresponding non-interacting systems may be insulating or metallic, we can say
that the gap originates from strong correlation. The persistent currents of the
present models are also investigated and found to be exactly vanishing.Comment: 59 pages, REVTeX 3.0, Figures are available on reques
The Short Range RVB State of Even Spin Ladders: A Recurrent Variational Approach
Using a recursive method we construct dimer and nondimer variational ansatzs
of the ground state for the two-legged ladder, and compute the number of dimer
coverings, the energy density and the spin correlation functions. The number of
dimer coverings are given by the Fibonacci numbers for the dimer-RVB state and
their generalization for the nondimer ones. Our method relies on the recurrent
relations satisfied by the overlaps of the states with different lengths, which
can be solved using generating functions. The recurrent relation method is
applicable to other short range systems. Based on our results we make a
conjecture about the bond amplitudes of the 2-leg ladder.Comment: REVTEX file, 32 pages, 10 EPS figures inserted in text with epsf.st
Determination of the basin of attraction of a periodic orbit in two dimensions using meshless collocation
A contraction metric for an autonomous ordinary differential equation is a Riemannian metric such that the distance between adjacent solutions contracts over time. A contraction metric can be used to determine the basin of attraction of a periodic orbit without requiring information about its position or stability. Moreover, it is robust to small perturbations of the system. In two-dimensional systems, a contraction metric can be characterised by a scalar-valued function. In [9], the function was constructed as solution of a first-order linear Partial Differential Equation (PDE), and numerically constructed using meshless collocation. However, information about the periodic orbit was required, which needed to be approximated. In this paper, we overcome this requirement by studying a second-order PDE, which does not require any information about the periodic orbit. We show that the second-order PDE has a solution, which defines a contraction metric. We use meshless collocation to approximate the solution and prove error estimates. In particular, we show that the approximation itself is a contraction metric, if the collocation points are dense enough. The method is applied to two examples
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