1,720,998 research outputs found
Mesh selection strategies of the code TOM for Boundary Value Problems
Full text linkThis paper presents new hybrid mesh selection strategies for boundary value problems
implemented in the code TOM. Originally the code was proposed for the numerical
solution of stiff or singularly perturbed problems. The code has been now improved
with the introduction of three classes of mesh selection strategies, that can be used for
different categories of problems. Numerical experiments show that the mesh selection
and, in the nonlinear case, the strategy for solving the nonlinear equations are determinant
for the good behaviour of a general purpose code. The possibility to choose
the mesh selection should be considered for all general purposes codes to make them
suitable for wider classes of problems
Correction to: "On a class of Hermite-Obreshkov one-step methods with continuous spline extension" [Axioms 7 (3), 58, 2018]
Full text linkThe authors of the above mentioned paper specify that the considered class of one-step symmetric Hermite-Obreshkov methods satisfies the property of conjugate-symplecticity up to order p + r, where r = 2 and p is the order of the method. This generalization of conjugate-symplecticity states that the methods conserve quadratic first integrals and the Hamiltonian function over time intervals of length O(h-r). Theorem 1 of the above mentioned paper is then replaced by a new one. All the other results in the paper do not change. Two new figures related to the already considered Kepler problem are also added
Classification of hyperspectral images with copulas
Full text linkIn the last decade, supervised learning methods for the classification of remotely sensed images (RSI) have grown significantly, especially for hyper-spectral (HS) images. Recently, deep learning-based approaches have produced encouraging results for the land cover classification of HS images. In particular, the Convolutional Neural Networks (CNN) and Recurrent Neural Networks (RNN) have shown good performance. However, these methods suffer for the problem of the hyperparameter optimization or tuning that requires a high computational cost; moreover, they are sensitive to the number of observations in the learning phase. In this work we propose a novel supervised learning algorithm based on the use of copula functions for the classification of hyperspectral images called CopSCHI (Copula Supervised Classification of Hyperspectral Images). In particular, we start with a dimensionality reduction technique based on Singular Value Decomposition (SVD) in order to extract a small number of relevant features that best preserve the characteristics of the original image. Afterward, we learn the classifier through a dynamic choice of copulas that allows us to identify the distribution of the different classes within the dataset. The use of copulas proves to be a good choice due to their ability to recognize the probability distribution of classes and hence an accurate final classification with low computational cost can be conducted. The proposed approach was tested on two benchmark datasets widely used in literature. The experimental results confirm that CopSCHI outperforms the state-of-the-art methods considered in this paper as competitors
“Numerical Approximation of Nonlinear BVP by means of BVMs”
No full textBoundary Value Methods (BVMs) would seem to be suitable candidates for the solution of nonlinear Boundary Value Problems (BVPs). They have been successfully used for solving linear BVPs together with a mesh selection strategy based on the conditioning of the linear systems. Our aim is to extend this approach so as to use them for the numerical approximation of nonlinear problems. For this reason, we consider the quasi-linearization technique that is an application of the Newton method to the nonlinear differential equation. Consequently, each iteration requires the solution of a linear BVP. In order to guarantee the convergence to the solution of the continuous nonlinear problem, it is necessary to determine how accurately the linear BVPs must be solved. For this goal, suitable stopping criteria on the residual and on the error for each linear BVP are given. Numerical experiments on stiff problems give rather satisfactory results, showing that the experimental code, called TOM, that uses a class of BVMs and the quasi-linearization technique, may be competitive with well known solvers for BVPs
On conjugate-symplecticity properties of a multi-derivative extension of the midpoint and trapezoidal methods
No full textConjugate symplecticity up to order p 2 of p-th one-step multi-derivative methods based on an extension of the midpoint and trapezoidal methods is proved. If compared with similar achievements obtained for the class of Euler-MacLauren and Hermite-Obreshkov methods, this result further confirm that multi-derivative methods, despite failing in achieving the symplecticity property, may play a significant role in the context of geometric integration. A numerical illustration has also been added
On the Classification of Hyperspectral Images with Different Copula Family
No full textIn the task of remote sensing, the Hyperspectral image (HSI) classification to analyze land cover is an established research topic. However, the nature of remote sensing data still poses several challenges including, the curse of dimensionality, the negligible number of samples during training or the presence of unbalanced data which makes learning difficult. Having a training set of pixels with the label of the assigned class, the operation that is performed in the classification of hyperspectral images is to assign a class label to each pixel in the test set based on the knowledge acquired with the training set. This paper discusses a new approach in the supervised classification of HS images considering the statistical tool of Copulas. Comparison with well-established techniques shows the good behaviour of this technique
Approximated Iterative QLP for Change Detection in Hyperspectral Images
No full textWe propose a matrix factorization algorithm based on the iterative Stewart’s QLP decomposition. In particular, provided a given threshold, only an automatically selected subspace is used to approximate the original dense matrix. The algorithm is validated on the change detection task for Hyperspectral Images (HSI). The extraction of information from HSI is an important field of research relevant to many applications. In the aerospace sector, for example, it is useful to monitor changes of the Earth surface, or to find salient information from urban geo-spatial data. Therefore, low rank approximation techniques play a fundamental role
A Fourth Order Symplectic and Conjugate-Symplectic Extension of the Midpoint and Trapezoidal Methods
Full text linkThe paper presents fourth order Runge–Kutta methods derived from symmetric Hermite–Obreshkov schemes by suitably approximating the involved higher derivatives. In particular, starting from the multi-derivative extension of the midpoint method we have obtained a new symmetric implicit Runge–Kutta method of order four, for the numerical solution of first-order differential equations. The new method is symplectic and is suitable for the solution of both initial and boundary value Hamiltonian problems. Moreover, starting from the conjugate class of multi-derivative trapezoidal schemes, we have derived a new method that is conjugate to the new symplectic method
An adaptive optimized Nyström method for second-order IVPs
Full text linkThis research work deals with the development, analysis, and implementation of an adaptive optimized one-step Nystrom method for solving second-order initial value problems of ODEs and time-dependent partial differential equations. The new method is developed through a collocation technique with a new approach for selecting the collocation points. An embedding-like procedure is used to estimate the error of the proposed optimized method. The current approach has been used to compute efficiently approximate solutions to general second-order IVPs. The numerical experiments demonstrate that the introduced error estimation and step-size control strategy presented in this manuscript have produced a good performance compared to some of the other existing numerical methods
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