A fuzzy logic based similarity measure is introduced as a criterion for the identification of structure in data. An important characteristic of the proposed approach is that cluster prototypes are formed and evaluated...
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A fuzzy logic based similarity measure is introduced as a criterion for the identification of structure in data. An important characteristic of the proposed approach is that cluster prototypes are formed and evaluated in the course of the optimization without any a-priori assumptions about the number of clusters. The intuitively straightforward compound optimization criterion of maximizing the overall similarity between data and the prototypes while minimizing the similarity between the prototypes is adopted. It is shown that the partitioning of the pattern space obtained in the course of the optimization is more intuitive than the one obtained for the standard FCM. The local properties of clusters (in terms of the ranking order of features in the multidimensional pattern space) are captured by the weight vector associated with each cluster prototype. The weight vector is then used for the construction of interpretable information granules.
Examines a nonoverlapping domain decomposition method based on the natural boundary reduction. Development of the D-N alternating algorithm; Studies the convergence of the D-N method for exterior spherical domain; Dis...
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Examines a nonoverlapping domain decomposition method based on the natural boundary reduction. Development of the D-N alternating algorithm; Studies the convergence of the D-N method for exterior spherical domain; Discussion of the discrete form of the D-N alternating algorithm.
Hamilton-Jacobiequation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference...
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Hamilton-Jacobiequation appears frequently in applications, e.g., in differential games and control theory, and is closely related to hyperbolic conservation laws[3, 4, 12]. This is helpful in the design of difference approximations for Hamilton-Jacobi equation and hyperbolic conservation laws. In this paper we present the relaxing system for HamiltonJacobiequations in arbitrary space dimensions, and high resolution relaxing schemes for Hamilton-Jacobi equation, based on using the local relaxation approximation. The schemes are numerically tested on a variety of 1D and 2D problems, including a problem related to optimal control problem. High-order accuracy in smooth regions, good resolution of discontinuities, and convergence to viscosity solutions are observed.
This paper deals with boundary value problems for linear uniformly elliptic systems. First the general linear uniformly elliptic system of the first order equations is reduced to complex form, and then the compound bo...
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This paper deals with boundary value problems for linear uniformly elliptic systems. First the general linear uniformly elliptic system of the first order equations is reduced to complex form, and then the compound boundary value problem for the complex equations of the first order is discussed. The approximate solutions of the boundary value problem are found by the variation-difference method, and the error estimates for the approximate solutions are *** the approximate method of the oblique derivative problem for linear uniformly elliptic equations of the second or der is introduced.
In this paper,we consider a kind of coupled nonlinear problem with Signorini contact *** solve this problem,we discuss a new coupling of finite element and boundary element by adding an auxiliary *** first derive an a...
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In this paper,we consider a kind of coupled nonlinear problem with Signorini contact *** solve this problem,we discuss a new coupling of finite element and boundary element by adding an auxiliary *** first derive an asymptotic error estimate of the approximation to the coupled FEM-BEM variational *** we design an iterative method for solving the coupled system,in which only three standard subproblems without involving any boundary integral equation are *** will be shown that the convergence speed of this iteration method is independent of the mesh size.
A general local C-m(m greater than or equal to 0) tetrahedral interpolation scheme by polynomials of degree 4m + 1 plus low order rational functions from the given data is proposed. The scheme can have either 4m + 1 o...
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A general local C-m(m greater than or equal to 0) tetrahedral interpolation scheme by polynomials of degree 4m + 1 plus low order rational functions from the given data is proposed. The scheme can have either 4m + 1 order algebraic precision if C-2m data at vertices and C-m data on faces are given or k + E[k/3] + 1 order algebraic precision if C-k (k less than or equal to 2m) data are given at vertices. The resulted interpolant and its partial derivatives of up to order m are polynomials on the boundaries of the tetrahedra.
Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations...
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Focuses on a study which determined the geometry meaning of the maxima of the CDT mathematical subproblem's dual function. Properties of trust region subproblem; Approximation of the CDT feasible region; Relations between the CDT problem and the trust region problem; Illustration of the geometry meaning of the jump parameter.
Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; N...
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Provides information on a study which presented a trust region approach for solving nonlinear constrained optimization. Algorithm of the trust region approach; Information on the global convergence of the algorithm; Numerical results of the study.
A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the s...
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A matrix splitting method is presented for minimizing a quadratic programming (QP) problem, and a general algorithm is designed to solve the QP problem and generates a sequence of iterative points. We prove that the sequence generated by the algorithm converges to the optimal solution and has an R-linear rate of convergence if the QP problem is strictly convex and nondegenerate, and that every accumulation point of the sequence generated by the general algorithm is a KKT point of the original problem under the hypothesis that the value of the objective function is bounded below on the constrained region, and that the sequence converges to a KKT point if the problem is nondegenerate and the constrained region is bounded.
This paper introduces a new concept of exceptional family forvariational inequality problems with a general convex constrained set. By using this new concept, the authors establish a general sufficient condition for t...
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This paper introduces a new concept of exceptional family forvariational inequality problems with a general convex constrained set. By using this new concept, the authors establish a general sufficient condition for the existence of a solution to the problem. This condition is weaker than many known solution conditions and it is also necessary for pseudomonotone variational inequalities. Sufficient solution conditions for a class of nonlinear complementarity problems with P0 mappings are also obtained.
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