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In this paper, we propose an Alternating Direction Method of Multipliers (ADMM) based algorithm that is taking advantage of factorization for the fixed rank matrix completion problem. The convergence of the proposed algorithm to the KKT point is discussed. Finally, on several classes of test problems, its efficiency is compared with several efficient algorithms from the literature. [ABSTRACT FROM AUTHOR]

In this paper, a de Casteljau algorithm to compute (p, q)-Bernstein B'ezier curves based on (p, q)-integers is introduced. We study the nature of degree elevation and degree reduction for (p, q)-B'ezier Bernstein functions. The new curves have some properties similar to q-B'ezier curves. Moreover, we construct the corresponding tensor product surfaces over the rectangular domain (u, v) ∈ [0, 1] × [0, 1] depending on four parameters. We also study the de Casteljau algorithm and degree evaluation properties of the surfaces for these generalization over the rectangular domain. Furthermore, some fundamental properties for (p, q)-Bernstein B'ezier curves are discussed. We get q-B'ezier curves and surfaces for (u, v) ∈ [0, 1] × [0, 1] when we set the parameters p1 = p2 = 1. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a random variational-like inclusion and its corresponding random proximal operator equation for random fuzzy mappings. It is established that the random variational-like inclusion problem for random fuzzy mappings is equivalent to a random fixed point problem. We also establish a relationship between random variational-like inclusion and random proximal operator equation for random fuzzy mappings. This equivalence is used to define an iterative algorithm for solving random proximal operator equation for random fuzzy mappings. Through an example, we show that the random Wardrop equilibrium problem is a special case of the random variational-like inclusion problem for random fuzzy mappings. [ABSTRACT FROM AUTHOR]

In this paper we prove convergence of the method of successive approximations used to approximate the solution of nonlinear two-dimensional Volterra-Fredholm integral equations and define the notion of numerical stability of the algorithm with respect to the choice of the first iteration. Also we present an iterative procedure to solve such equations. Finally, the method is illustrated by solving some examples. [ABSTRACT FROM AUTHOR]

In this paper, we presented a fitted approach to solve singularly perturbed differential difference equations of second order with boundary at one end (left or right) of the interval. In this approach, with the help of Taylor series expansion, we approximated the terms containing negative and positive shifts and modified the singularly perturbed differential difference equation to singularly perturbed differential equation. A fitting parameter in the coefficient of the highest order derivative of the new equation is introduced and determined its value from the theory of singular perturbation. Finally, we obtained a three term recurrence relation which is solved using Thomas Algorithm. The applicability of the method is tested with six linear problems. [ABSTRACT FROM AUTHOR]

Linear systems arise frequently in scientific and engineering computing. Various serial and parallel algorithms have been introduced for their solution. This paper seeks to compute the WZ and the ZW factorizations of a nonsingular matrixA using the right inverse of nested submatrices of A. We introduce two new matrix factorizations, the QZ and the QW factorizations, and compute the factorizations using our proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a new combined extended Conjugate-Gradient (CG) and Variable-Metric (VM) methods is proposed for solving unconstrained large-scale numerical optimization problems. The basic idea is to choose a combination of the current gradient and some pervious search directions as a new search direction updated by Al-Bayati's SCVM-method to fit a new step-size parameter using Armijo Inexact Line Searches (ILS). This method is based on the ILS and its numerical properties are discussed using different non-linear test functions with various dimensions. The global convergence property of the new algorithm is investigated under few weak conditions. Numerical experiments show that the new algorithm seems to converge faster and is superior to some other similar methods in many situations. [ABSTRACT FROM AUTHOR]

In this paper, we use the shifted Jacobi polynomials to approximate the solution of the space fractional advection-dispersion. The method is based on the Jacobi operational matrices of fractional derivative and integration. A double shifted Jacobi expansion is used as an approximating polynomial. We apply this method to solve linear and nonlinear term FDEs by using initial and boundary conditions. [ABSTRACT FROM AUTHOR]

We address the problem of finding a 1-median on a cactus graph. The problem has already been solved in linear time by the algorithms of Burkard and Krarup (1998), and Lan and Wang (2000). These algorithms are complicated and need efforts. Hence, we develop in this paper a simpler algorithm. First, we construct a condition for a cycle that contains a 1-median or for a vertex that is indeed a 1-median of the cactus. Based on this condition, we localize the search for deriving a 1-median on the underlying cactus. Complexity analysis shows that the approach runs in linear time. [ABSTRACT FROM AUTHOR]

In this paper, we consider all the Janko sporadic groups J1, J2, J3 and J4 (with orders 175560, 604800, 50232960 and 86775571046077562880, respectively) with a new concept called the markaracter- and Q-conjugacy character tables, which enables us to discuss marks and characters for a finite group on a common basis of Q-conjugacy relationships between their cyclic subgroups. Then by using GAP (Groups, Algorithms and Programming) package we calculate all their dominant classes enabling us to find all possible Q-conjugacy characters for these sporadic groups. Finally, we prove in a main theorem that all twenty six simple sporadic groups are unmatured. [ABSTRACT FROM AUTHOR]

This study presents a hybrid algorithm consisting of game theory and the first order Taylor series approach to find compromise solutions to multi-objective linear fractional programming (MOLFP) problems. The proposed algorithm consists of three phases including different techniques: in the first phase, the optimal solution to each LFP problem is found using the simplex method; in the second phase, a zero-sum game is solved to determine the weights of the objective functions via the ratio matrix obtained from a payoff matrix; in the last phase, fractional objective functions of the MOLFP problem are linearized using the 1st order Taylor series. A compromise solution is found by solving the single-objective LP problem constructed in the third phase by using the weights. This algorithm can provide compromise solutions to the problem by constructing different ratio matrices in the second phase. The novelty of this study is that the decision-makers can choose the most suitable solution for their strategy among the compromise solutions. Numerical examples are provided to illustrate the efficiency of the algorithm. [ABSTRACT FROM AUTHOR]

This study aims at constructing a numerical scheme for solving singularly perturbed parabolic delay differential equations. Taylor’s series expansion is applied to approximate the shift term. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is an ε−uniformly convergent accuracy of order one. Some test examples are considered to testify the theoretical investigations. [ABSTRACT FROM AUTHOR]

The primary focus of this manuscript comprises three sections. Initially, we introduce the concept of a simplified intuitionistic neutrosophic soft set. We impose an intuitionistic condition between the membership values of truth and falsity such that their sum does not exceed unity. Similarly, for indeterminacy, the membership value is a real number from the closed interval [0, 1]. Hence, the sum of membership values of truth, indeterminacy, and falsity does not exceed two. We present the notion of necessity, possibility, concentration, and dilation operators and establish some of its properties. Second, we define the similarity measure between two simplified intuitionistic neutrosophic soft sets. Also, we discuss its superiority by comparing it with existing methods. Finally, we develop an algorithm and illustrate with an example of diagnosing psychological disorders. Even though the similarity measure plays a vital role in diagnosing psychological disorders, existing methods deal hardly in diagnosing psychological disorders. By nature, most of the psychological disorder behaviors are ambivalence. Hence, it is vital to capture the membership values by using simplified intuitionistic neutrosophic soft set. In this manuscript, we provide a solution in diagnosing psychological disorders, and the proposed similarity measure is valuable and compatible in diagnosing psychological disorders in any neutrosophic environment. [ABSTRACT FROM AUTHOR]

In this article a direct method is introduced, which is based on orthonormal Bernstein polynomials, to present an efficient and stable algorithm for numerical inversion of the system of singular integral equations of Abel type. The appropriateness of earlier numerical inversion methods was restricted to the one portion of singular integral equations of Abel type. The proposed method is absolutely accurate, and numerical illustrations are given to show the convergence and utilization of the suggested method and comparisons are made with some other existing numerical solution. [ABSTRACT FROM AUTHOR]

A high accurate spectral algorithm for one-dimensional variable-order fractional percolation equations (VO-FPEs) is considered. We propose a shifted Legendre Gauss-Lobatto collocation (SL-GLC) method in conjunction with shifted Chebyshev Gauss-Radau collocation (SC-GR-C) method to solve the proposed problem. Firstly, the solution and its space fractional derivatives are expanded as shifted Legendre polynomials series. Then, we determine the expansion coefficients by reducing the VO-FPEs and its conditions to a system of ordinary differential equations (SODEs) in time. The numerical approximation of SODEs is achieved by means of the SC-GR-C method. The under-study's problem subjected to the Dirichlet or non-local boundary conditions is presented and compared with the results in literature, which reveals wonderful results. [ABSTRACT FROM AUTHOR]

Lemke's algorithm is a pivotal kind of algorithm which is developed based on principal pivot transform. We consider several matrix classes to study the relationship among them in the context of linear complementarity problem. These classes are important from Lemke's algorithmic point of view. In this article we discuss about the processability of Lemke's algorithm with respect to some selective matrix classes. [ABSTRACT FROM AUTHOR]

We introduce a method for aggregation of experts' opinions given in the form of comparative linguistic expression. An algorithmic form of technique for order preference is proposed for group decision making. A simple example is given by using this method for the selection of the best alternative as well as ranking the alternatives from the best to the worst. [ABSTRACT FROM AUTHOR]