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Matsumoto, Saito and Matoba recently proposed the Walsh figure of merit (WAFOM), which is a computable criterion for quasi-Monte Carlo point sets using digital nets. Several algorithms have been proposed for finding low-WAFOM point sets. In the existing algorithms, the number of points is fixed in advance, but extensible point sets are preferred in some applications. In this paper, we propose a random search algorithm for extensible low-WAFOM point sets. For this, we introduce a method that uses lookup tables to compute WAFOM faster. Numerical results show that our extensible low-WAFOM point sets are comparable with Niederreiter-Xing sequences for some low-dimensional and smooth test functions. [ABSTRACT FROM AUTHOR]

This is a review paper of the role of Carleman estimates in the theory of multidimensional coefficient inverse problems since the first inception of this idea in 1981. [ABSTRACT FROM AUTHOR]

In this paper, we describe a stochastic algorithm to solve sudoku puzzles. Our method consists in computing probabilities for each symbol of each cell updated at each step of the algorithm using estimation of distributions algorithms (EDA). This update is done using the empirical estimators of these probabilities for a fraction of the best puzzles according to a cost function. We develop also some partial restart techniques in the RESEDA algorithm to obtain a convergence for the most difficult puzzles. Our algorithm is tested numerically on puzzles with various levels of difficulty starting from very easy ones to very hard ones including the famous puzzle AI Escargot. The CPU times vary from few hundreds of a second for the easy ones to about one minute for the most difficult one. [ABSTRACT FROM AUTHOR]

In the paper we present several numerical algorithms to simulate the fractional Brownian motion (the generalized Wiener process). The algorithms have been developed on the basis of the integral representation of the fractional Brownian motion and the spectral decomposition for its increments. The convergence of the numerical methods has been studied. [ABSTRACT FROM AUTHOR]

In this paper we propose a numerical method for solving nonstationary Maxwell equations on unstructured triangular grids, which is based on the finite volume method. We give the results of test calculations which confirm the second order of convergence of the method both for homogeneous media and media with space-variable dielectric permittivity. [ABSTRACT FROM AUTHOR]

In this paper we propose an improved quasi-Monte Carlo method for solving Linear Algebra problems. We show that by using low-discrepancy sequences both the convergence and the CPU time of the algorithm are improved. Two parallelization schemes using the Message Passing Interface with static and dynamic load balancing are proposed. The dynamic scheme is useful for computing in the GRID environment. [ABSTRACT FROM AUTHOR]

In recent years, the question on the convergence and optimality in the context of adaptive finite element methods has been the subject of intensive studies. However, for nonstandard FEMs such as mixed or nonconforming ones, the lack of Gaierkin's orthogonality requires new mathematical arguments. The presented adaptive algorithm for the Crouzeix-Raviart finite element method and the Poisson model problem is of quasi-optimal complexity. Furthermore it is natural in the sense that collective marking rather than a separate marking is applied or the estimated error and the volume term. [ABSTRACT FROM AUTHOR]

We consider a predictor-corrector type finite difference scheme for solving one-dimensional parabolic problems. This algorithm decouples computations on different subdomains and thus can be efficiently implemented on parallel computers and used to solve problems on graph structures. The stability and convergence of the discrete solution is proved in the special energy and maximum norms. The results of computational experiments are presented. [ABSTRACT FROM AUTHOR]

Iterative methods for finite-dimensional inclusions which arise in applying a finite-element or a finite-difference method to approximate state-constrained optimal control problems have been investigated. Specifically, problems of control on the right-hand side of linear elliptic boundary value problems and observation in the entire domain have been considered. The convergence and the rate of convergence for the iterative algorithms based on the finding of the control function or Lagrange multipliers are proved. [ABSTRACT FROM AUTHOR]

We consider the conforming of finite element approximations of reaction-diffusion problems. We propose new a posteriori error estimators based on H(div)- conforming finite elements and equilibrated fluxes. It is shown that these estimators give rise to an upper bound where the constant is one in front of the indicator, up to higher order terms. Lower bounds can also be established with constants depending on the shape regularity of the mesh and the local variation of the coefficients. We further analyze the convergence of an adaptive algorithm. The reliability and efficiency of the proposed estimators are confirmed by various numerical tests. [ABSTRACT FROM AUTHOR]

In this study, we apply optimal control approaches and adjoint equations to construct iterative processes for some problems of hydrodynamics. First, the iterative processes are proposed for an abstract problem given by the system of operator equations. Second, the general methodology is applied to the generalized Stokes equations perturbed by a skew-symmetric bounded operator and to the stationary linearized Navier–Stokes equations (the Oseen problem). The convergence rates of the iterative algorithms are studied. [ABSTRACT FROM AUTHOR]