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On the best constant in the inf-sup-condition for elongated rectangular domains

MATHEMATICAL NOTES 2000年第3-4期67卷 325-332页

作者： Ol'shanskii, MA Chizhonkov, EV Moscow MV Lomonosov State Univ Moscow 117234 Russia

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.

关键词： inf-sup-condition Stokes equation boundary problem computational hydrodynamics efficiency of algorithms

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ON SOLVING OPERATOR-EQUATIONS BY MULTIPOINT ITERATIVE METHODS

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INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 1986年第1期20卷 77-90页

作者： MORET, I UNIV TRIESTE DIPARTIMENTO ELETTROTECN ELETTR & INFORMAT I-34100 TRIESTE ITALY

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.

关键词： Iterative methods non-linear equations efficiency of algorithms 5.15 5.25

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Accelerating MCMC algorithms

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WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL STATISTICS 2018年第5期10卷 e1435-e1435页

作者： Robert, Christian P. Elvira, Victor Tawn, Nick Wu, Changye PSL Res Univ Univ Paris Dauphine Paris France Univ Warwick Dept Stat Coventry W Midlands England IMT Lille Douai Douai France CRIStAL Lille France

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

关键词： Bayesian analysis computational statistics convergence of algorithms efficiency of algorithms Hamiltonian Monte Carlo Monte Carlo methods Rao-Blackwellisation simulation tempering

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The basic element method

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Mathematical Models and Computer Simulations 2011年第4期3卷 492-507页

作者： Dikusar, N.D. Joint Institute for Nuclear Research Laboratory of Information Technologies Moscow Russian Federation

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 the polynomial via basic elements gives a lever for solving various tasks of applied mathematics. So, in the polynomial approximation and smoothing problems, the BEM allows one to reduce the computational complexity of algorithms and increase their resistance to errors by choosing an internal relationship structure between variable and control parameters. © 2011, Pleiades Publishing, Ltd.

关键词： approximation by polynomials data smoothing efficiency of algorithms four-point transformation least squares method linear regression

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Higher-order polynomial approximation

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Mathematical Models and Computer Simulations 2016年第2期8卷 183-200页

作者： Dikusar, N.D. Laboratory of Information Technologies Joint Institute for Nuclear Research Dubna 141980 Russian Federation

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: x₀ + α < x₀ < x₀ + β, αβ <0. Formulas for the calculation of coefficients of the polynomial model of order 12 were derived. These formulas depend on the interval length, continuous parameters α and β, and the values of f^(m)(x₀+ν), ν = α, β, 0, m = 0,3. The application of higher-degree BEM polynomials in piecewise-polynomial approximation and smoothing improves the stability and accuracy of calculations when the grid step is increased and reduces the computational complexity of the algorithms. © 2016, Pleiades Publishing, Ltd.

关键词： basic elements method curve segmentation efficiency of algorithms higher-degree polynomials least squares method piecewise-polynomial approximation smoothing

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Finding Two Disjoint Paths Between Two Pairs of Vertices in a Graph

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Journal of the ACM (JACM) 1978年第1期25卷 1-9页

作者： Shiloach, Y. Perl, Y. Weizmann Institute of Science Rehovot Israel Computer Science Department Stanford University Stanford CA United States Department of Mathematics and Computer Science Bar-Ilan University Ramat-Gan Israel

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 and m printed clrcmts routing The relations between several vemons of the problem are discussed Efficient algorithms are gwen for the following special cases-acyche directed graphs and 3-connected planar and chordal graphs. © 1978, ACM. All rights reserved.

关键词： acychc directed graphs chordal graphs connectivtty disjoint paths efficiency of algorithms graph algorithms networks pairs of vertices planar graphs polynomial reductions routing transportation

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Piecewise polynomial approximation of the sixth order with automatic knots detection

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Mathematical Models and Computer Simulations 2014年第5期6卷 509-522页

作者： Dikusar, N.D. Joint Institute for Nuclear Research Laboratory of Information Technologies ul. Joliot Curie 6 Dubna Moscow 141980 Russian Federation

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 coefficients of the function’s expansion in degrees of x-x₀ on a three-point grid are obtained within the recently proposed basic element method. The algorithm for automatic knot detection is developed. Numerical calculations applying quite complicated tests have shown the efficiency of the model with respect to calculation stability, accuracy, and smoothness of approximation. © 2014, Pleiades Publishing, Ltd.

关键词： basic elements method efficiency of algorithms interpolation least squares method optimal selection of knots piecewise polynomial approximation smoothing

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STRONG CONVERGENCE ANALYSIS FOR SOLVING QUASI-MONOTONE VARIATIONAL INEQUALITIES AND FIXED POINT PROBLEMS IN REFLEXIVE BANACH SPACES

JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS

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JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS 2023年第1期2023卷

作者： Owolabi, A. O. E. Mewomo, O. T. Yao, J. C. Qin, X. Univ KwaZulu Natal Sch Math Stat & Comp Sci Durban South Africa China Med Univ Ctr Gen Educ Taichung Taiwan Acad Romanian Scientists Bucharest 50044 Romania Kyung Hee Univ Ctr Adv Informat Technol Seoul 02447 South Korea

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.

关键词： . Bregman distance efficiency of algorithms Numerical experiments Quasi-monotone variational inequalities Self-adaptive step sizes

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