Lopez de Hierro, A. F. RoldanSanchez, M.Roldan, C.
15页
查看更多>>摘要：Many advances in artificial intelligence and machine learning are based on decision making, especially in uncertain settings. Due to its possible applications, decision making is currently a broad field of study in many areas like Computation, Economics and Business Management. The first techniques appeared in scenarios where information was modeled by real numbers. In all cases, one of the key steps in such processes was the summarization of the available information into a few values that helped the decision maker to complete this task. In this paper, we introduce a novel multi-criteria decision making methodology in the fuzzy context in which weights and experts' opinions (may be translated by linguistic labels) are stated as triangular fuzzy numbers. To do that, we take advantage of a recently presented fuzzy binary relation whose properties are according to human intuition and we carry out a study of the main properties that an aggregation function (a mapping to sum up information) must satisfy in the fuzzy framework. The presented procedure makes a final decision based on parabolic fuzzy numbers (not triangular). And this will be shown in an illustrative example.(c) 2020 Elsevier B.V. All rights reserved.
Hernandez-Veron, M. A.Martinez, EulaliaSingh, Sukhjit
13页
查看更多>>摘要：This work is devoted to solve integral equations formulated in terms of the kernel functions and Nemytskii operators. This type of equations appear in different applied problems such as electrostatics and radiative heat transfer problems. We deal with both cases separable and non-separable kernels by setting the theoretical semilocal convergence results for an adequate iterative scheme that can be useful for approximating the solution of the infinite dimensional problem. We pay special attention to non-separable kernels avoiding the solution given in previous works where the original nonlinear integral equation has been approximated by means of an equation with separable kernel. However, in this case, we introduce an approximation of the derivative operator that it is needed for applying the iterative scheme considered. Moreover, we study the localization and separation of possible solutions of nonlinear integral equation by means of a result of semilocal convergence for the iterative scheme considered. The theoretical results obtained have been tested with some applied problems showing competitive results. (c) 2020 Elsevier B.V. All rights reserved.
查看更多>>摘要：We consider a Levenberg-Marquardt method for solving nonlinear inverse problems in Hilbert spaces. The proposed method uses general convex penalty terms to reconstruct nonsmooth solutions of inverse problems. Instead of an a priori choice, the regularization parameter in each iteration is chosen by solving an equation which depends on the residual. We utilize the discrepancy principle to terminate the iteration and give the convergence results. In addition, numerical simulations are presented to test the performance of the method. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this work, we use Newton-type iterative schemes to obtain a domain of existence of solution, approximate the solution of Chandrasekhar H-equations and deal with the case of nonlinear integral equations with non-separable kernels. A change of variable in the Chandrasekhar H-equation allows us to apply a previous study by describing nonlinear integral equations of Hammerstein-type with non-separable kernel. We use the Bernstein polynomials for approximating the non-separable kernel and then we apply a semilocal converge study done previously to the Chandrasekhar H-equation. Moreover, we apply Newton-type iterative schemes for some specific Chandrasekhar H-equations to approximate the H-function solution and compare our results with others obtained previously. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we propose a new approximation algorithm for solving generalized Lyapunov matrix equations. We also present a convergence analysis for this algorithm. In each step of this algorithm two standard Lyapunov matrix equations with real coefficient matrices should be solved. Then we determine the optimal parameter to minimize the corresponding spectral radius of iteration matrix to obtain fastest speed of convergence. Finally some numerical examples are given to prove the capability of the present algorithm and a comparison is made with the existing results. (C) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we present a new three-point iterative scheme for obtaining the solution of nonlinear system having seventh-order convergence. The beauty of our scheme is that we obtained the seventh-order convergence with minimal computational cost as compared to the existing ones. In addition, we also analyze the theoretical convergence properties of the proposed scheme. Moreover, we show its applicability on a total six numbers of nonlinear models: first three of them are boundary value, Hammerstein integral and 2D Bratu's problems; the last three are standard academic large systems of nonlinear equations of order 50 x 50, 100 x 100 and 120 x 120, respectively. Finally, we concluded on the basis of obtained numerical experiments that our iterative method performs better in terms of residual error, computational efficiency, error between the two consecutive iterations, CPU-time, asymptotic error constant term and approximated root. (C)& nbsp;2020 Elsevier B.V. All rights reserved.
Calvo-Jurado, CarmenCasado-Diaz, JuanLuna-Laynez, Manuel
21页
查看更多>>摘要：We extend to a non-periodic framework the classical homogenization result permitting to derive the Darcy law from the Stokes or Navier-Stokes system posed in a perforated domain. Mathematically, we study the asymptotic behavior when epsilon tends to zero of the stationary Stokes system posed in a sequence of varying domains Omega(epsilon) = Omega \ boolean OR T-k is an element of N(epsilon)k where Omega is a smooth bounded open subset of R-3 and T-epsilon(k) are closed sets such that each of them is at a distance of order epsilon of the remaining. Moreover boolean OR T-k is an element of N(epsilon)k is at a distance of order at most epsilon of any point of R-3. Each set T-epsilon(k) is non-empty, smooth and has a size of order delta(epsilon) with epsilon(3) << delta(epsilon) <= r epsilon for some r < 1. In the classical periodic case, the sets T-epsilon(k) are obtained by repeating periodically with period epsilon the set delta T-epsilon with T a non-empty smooth closed set in R-3. As in this periodic case we show that the limit problem corresponds to a Darcy system. However, even when the sets T-epsilon(k) have all the same shape, we show that for delta(epsilon) << epsilon some strong convergence results for the velocity and some capacity formulae for the limit system do not extend from the periodic framework to the non-periodic one. (c) 2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：We define a family of univariate many knot spline spaces of arbitrary degree defined on an initial partition that is refined by adding a point in each sub-interval. For an arbitrary smoothness r, splines of degrees 2r and 2r + 1 are considered by imposing additional regularity when necessary. For an arbitrary degree, a B-spline-like basis is constructed by using the Bernstein-Bezier representation. Blossoming is then used to establish a Marsden's identity from which several quasi-interpolation operators having optimal approximation orders are defined. (C)& nbsp;2021 Elsevier B.V. All rights reserved.
查看更多>>摘要：In this paper, we presented a novel and efficient fourth order derivative free optimal family of iterative methods for approximating the multiple roots of nonlinear equations. Initially the convergence analysis is performed for particular values of multiple roots afterward it concludes in general form. In addition, we study several numerical experiments on real life problems in order to confirm the efficiency and accuracy of our methods. We illustrate the applicability and comparisons of our methods on eigenvalue problem, Van der Waals equation of state, continuous stirred tank reactor (CSTR), Plank's radiation and clustering problem of roots with earlier robust iterative methods. Finally, on the basis of obtained computational results, we conclude that our methods perform better than the existing ones in terms of CPU timing, absolute residual errors, asymptotic error constants, absolute error difference between two last consecutive iterations and approximated roots compared to the existing ones. (C)& nbsp;2021 Published by Elsevier B.V.
查看更多>>摘要：In this work, we propose a numerical finite element discretization with strong mass conservation for the coupled Stokes and dual-porosity model. Based on divergence conforming finite element spaces and piecewise discontinuous finite element spaces, this strongly conservative discretization is constructed by utilizing the symmetric interior penalty Galerkin method and mixed finite element method to discrete the governing equations of Stokes region and dual-porosity domain, respectively. In light of a discrete inf-sup condition, we present the well-posedness of discrete scheme and prove priori error estimates. After using uniformly matching meshes and the lower order finite element spaces of velocity and pressure, some numerical examples are given to validate the analysis of convergence and strong mass conservation. Further, these numerical results support our findings and illustrate the applicability of the coupled Stokes-dual-porosity model. (C) 2021 Elsevier B.V. All rights reserved.
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