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We consider the problem of tensor (i.e., multidimensional array) inpainting in this paper. By using higher-order singular value decomposition, we propose an iterative algorithm that performs soft thresholding on entries of the core tensor and then reconstructs via the directional orthogonal matrices. An inpainted tensor is obtained at the end of the iteration. Simulations conducted over color images, video frames, and MR images validate that the proposed algorithm is competitive with state-of-the-art completion algorithms. The evaluation is made in terms of quality metrics and visual comparison. [ABSTRACT FROM AUTHOR]

In this paper, we propose two iterative methods for finding a common solution of a finite family of equilibrium problems for pseudomonotone bifunctions. The first is a parallel hybrid extragradientcutting algorithm which is extended from the previously known one for variational inequalities to equilibrium problems. The second is a new cyclic hybrid extragradient-cutting algorithm. In the cyclic algorithm, using the known techniques, we can perform and develop practical numerical experiments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm to approximate fixed points of total asymptotically nonexpansive mappings in $\operatorname{CAT}(0)$ spaces. We also provide two examples to illustrate the convergence behavior of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing schemes. [ABSTRACT FROM AUTHOR]

In this paper, an efficient algorithm is established for computing the maximum (minimum) angular separation ρ( ρ), the corresponding apparent position angles ( $\theta|_{\rho_{\rm max}}$, $\theta|_{\rho_{\rm min}}$) and the individual masses of visual binary systems. The algorithm uses Reed's formulae (1984) for the masses, and a technique of one-dimensional unconstrained minimization, together with the solution of Kepler's equation for $(\rho_{\rm max}, \theta|_{\rho_{\rm max}})$ and $(\rho_{\rm min}, \theta|_{\rho_{\rm min}})$. Iterative schemes of quadratic coverage up to any positive integer order are developed for the solution of Kepler's equation. A sample of 110 systems is selected from the Sixth Catalog of Orbits (Hartkopf et al.). Numerical studies are included and some important results are as follows: (1) there is no dependence between ρ and the spectral type and (2) a minor modification of Giannuzzi's () formula for the upper limits of ρ functions of spectral type of the primary. [ABSTRACT FROM AUTHOR]

Fast multipole boundary element methods (FMBEMs) are developed based on the couple of fast multipole algorithm and generalized minimal residual algorithm. The FMBEMs improve the efficiency of conventional BEMs, accelerate the computing, enlarge the solving scale, and it is applied in various engineering fields. The paper tried to do a brief review for the FMBEMs, and focus on the description of basic principles and applications in rolling engineering. The basic principles and main frameworks of two typical methods of FMBEMs (sphere harmonic function multipole BEM and Taylor series multipole BEM) are briefly described, and then the key numerical iterative and preconditioning techniques suitable for the FMBEMs are introduced. The typical numerical examples are presented, including the elasticity problems, the elastic contact problems and the elastoplasticity problems, etc. The validity and effectiveness of FMBEMs are effectively illustrated by engineering analysis examples. The numerical results suggest that the FMBEMs are suitable for the analysis and solution of large scale rolling engineering problems. The implementation process of numerical analysis can provide useful reference for the applications in other engineering fields. [ABSTRACT FROM AUTHOR]

Solving large sparse linear systems is essential in numerous scientific domains. Several algorithms, based on direct or iterative methods, have been developed for parallel architectures. On distributed grids consisting of processors located in distant geographical sites, their performance may be unsatisfactory because they suffer from too many synchronizations and communications. The GREMLINS code has been developed for solving large sparse linear systems on distributed grids. It implements the multisplitting method that consists in splitting the original linear system into several subsystems that can be solved independently. In this paper, the performance of the GREMLINS code obtained with several libraries for solving the linear subsystems is analyzed. Its performance is also compared with that of the widely used PETSc library that enables one to develop portable parallel applications. Numerical experiments have been carried out both on local clusters and on distributed grids. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical treatment of inverse heat conduction problems. In particular, we combine recent results on the regularization of ill-posed problems by iterated soft shrinkage with adaptive wavelet algorithms for the forward problem. The analysis is applied to an inverse parabolic problem that stems from the industrial process of melting iron ore in a steel furnace. Some numerical experiments that confirm the applicability of our approach are presented. [ABSTRACT FROM AUTHOR]

The construction of the iteration procedure for synthesizing the law of control of observation over the processes, appeared one after another according to random flux regularities, is considered. The general approach to solution of the problem and the approximate algorithm for synthesizing the law of observations control are given for the case of a simple Poissonian flux. The example is presented in the paper. [ABSTRACT FROM AUTHOR]

This paper describes a numerical procedure for solving two-dimensional elastostatics problems with multiple circular holes and elastic inclusions in a finite domain with a circular boundary. The inclusions may have arbitrary elastic properties, different from those of the matrix, and the holes may be traction free or loaded with uniform normal pressure. The loading can be applied on all or part of the finite external boundary. Complex potentials are expressed in the form of integrals of the tractions and displacements on the boundaries. The unknown boundary tractions and displacements are approximated by truncated complex Fourier series. A linear algebraic system is obtained by using Taylor series expansion without boundary discretization. The matrix of the linear system has diagonal submatrices on its diagonal, which allows the system to be effectively solved by using a block Gauss-Seidel iterative algorithm. [ABSTRACT FROM AUTHOR]