The Ladyzhenskaya-Babushka-Brezzi inequality (inf-sup-condition) is often used in the analysis of convergence of approximate solutions of hydrodynamic equations to exact ones. The constant involved in it depends on th...
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The Ladyzhenskaya-Babushka-Brezzi inequality (inf-sup-condition) is often used in the analysis of convergence of approximate solutions of hydrodynamic equations to exact ones. The constant involved in it depends on the shape of the domain and determines the efficiency of different algorithms. In this paper, its asymptotics and two-sided estimates for rectangular domains are obtained. To this end, a new method for estimating eigenvalues of a certain spectral problem with Stokes' saddle operator is used.
Multipoint iterative procedures for solving non-linear operator equations in Banach spaces are considered. They are described by a general iteration scheme (1.2) which extends that proposed by Wolfe. Local convergence...
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Multipoint iterative procedures for solving non-linear operator equations in Banach spaces are considered. They are described by a general iteration scheme (1.2) which extends that proposed by Wolfe. Local convergence and order of convergence are studied. Moreover error estimates are given. A classical efficiency measure is introduced and criteria for comparing the efficiencies of different families of multipoint iterative methods are established. Later these criteria are applied to some interesting particular cases.
Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the natur...
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Markov chain Monte Carlo algorithms are used to simulate from complex statistical distributions by way of a local exploration of these distributions. This local feature avoids heavy requests on understanding the nature of the target, but it also potentially induces a lengthy exploration of this target, with a requirement on the number of simulations that grows with the dimension of the problem and with the complexity of the data behind it. Several techniques are available toward accelerating the convergence of these Monte Carlo algorithms, either at the exploration level (as in tempering, Hamiltonian Monte Carlo and partly deterministic methods) or at the exploitation level (with Rao-Blackwellization and scalable methods). This article is categorized under: Statistical and Graphical Methods of Data Analysis > Markov Chain Monte Carlo (MCMC) algorithms and Computational Methods > algorithms Statistical and Graphical Methods of Data Analysis > Monte Carlo Methods
The basic element method (BEM) for decomposition of the algebraic polynomial via one cubic and three quadratic parabolas (basic elements) is developed within the four-point transformation technique. Representation of ...
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A new approach to polynomial higher-order approximation (smoothing) based on the basic elements method (BEM) is proposed. A BEM polynomial of degree n is defined by four basic elements specified on a three-point grid:...
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Gwen a graph G = (V, E) and four verttces s1, t2, s2, and t2, the problem of finding two disjoint paths, P1 from s2 to t2 and P2 from s2 to t2, is considered This problem may arise as a transportation network problem ...
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Coefficients of a local segment model for piecewise polynomial approximation of the sixth order are evaluated using values of the function and of its first derivative at three knots of the support. The formulas for co...
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In this paper, we propose a modified inertial hybrid Tseng's extragradient algorithm with self-adaptive step sizes for finding a common solution of variational inequalities with quasimonotone operators and the fix...
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In this paper, we propose a modified inertial hybrid Tseng's extragradient algorithm with self-adaptive step sizes for finding a common solution of variational inequalities with quasimonotone operators and the fixed point problems of a finite family of Bregman quasi-nonexpansive mappings. By using the Bregman-distance approach, we prove a strong convergence result under some appropriate conditions on the control parameters in real reflexive Banach spaces. Our algorithm is based on a self-adaptive step size which generates a non-monotonic sequence. Unlike the existing results in the literature, our algorithm does not require any linesearch technique which uses inner loops and might consume additional computational time for determining the step size. Finally, we present some numerical examples to illustrate the efficiency of our algorithm in comparison with related methods in the literature.
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