Search

A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid. The rational interpolant is of the formmotivated by Tan and Fang (2000), which is combined by Newton interpolant and branched continued fractions, with scalar denominator. The matrix quotients are based on the generalized inverse for a matrixwhich is introduced by C. Gu the author of this paper, and it is effective in continued fraction interpolation. The algorithm and some other important conclusions such as divisibility and characterization are given. In the end, two examples are also given to show the effectiveness of the algorithm. The numerical results of the second example show that the algorithm of this paper is better than the method of Thieletype matrix-valued rational interpolant in Gu (1997). [ABSTRACT FROM AUTHOR]

The purpose of this paper is using Korpelevich's extragradient method to study the existence problem of solutions and approximation solvability problem for a class of systems of finite family of general nonlinear variational inequality in Banach spaces, which includes many kinds of variational inequality problems as special cases. Under suitable conditions, some existence theorems and approximation solvability theorems are proved. The results presented in the paper improve and extend some recent results. [ABSTRACT FROM AUTHOR]

In this paper, we develop a modified gradient based algorithm for solving matrix equations AXB + CXTD = F. Different from the gradient based method introduced by Xie et al., 2010, the information generated in the first half-iterative step is fully exploited and used to construct the approximate solution. Theoretical analysis shows that the new method converges under certain assumptions. Numerical results are given to verify the efficiency of the new method. [ABSTRACT FROM AUTHOR]

This paper addresses a new performance measure for scheduling problems, entitled "biased tardiness penalty." We study the approximability of minimum biased tardiness on a single machine, provided that all the due dates are equal. Two heuristic algorithms are developed for this problem, and it is shown that one of them has a worst-case ratio bound of 2. Then, we propose a dynamic programming algorithm and use it to design an FPTAS. The FPTAS is generated by cleaning up some states in the dynamic programming algorithm, and it requires O(n3/ε) time. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of the minimum length link scheduling (MLLS) in multiuser MIMO (MU-MIMO) networks. Generally, in the networks with MU-MIMO capability, the number of concurrent transmissions can be as large as that of antenna elements at the receiver. As a result, link interference is no longer binary but demonstrates a strong correlation among multiple links, which cannot be captured by the conventional conflict graph interference model. Hence, we propose a novel hypergraph interference model, which can accurately and efficiently characterize the relationship of multiple interferences induced by concurrent transmissions, and provide a tractable formalization of the minimumlength link scheduling in MU-MIMO networks (MU-MIMO MLLS). Afterwards, we prove that the MU-MIMO MLLS problem is NP-hard and introduce two approximation algorithms to find the near-optimal feasible schedule. Finally, extensive simulation experiments are presented. [ABSTRACT FROM AUTHOR]

This paper proposes some diagonal matrices that approximate the (inverse) Hessian by parts using the variational principle that is analogous to the one employed in constructing quasi-Newton updates. The way we derive our approximations is inspired by the least change secant updating approach, in which we let the diagonal approximation be the sum of two diagonal matrices where the first diagonal matrix carries information of the local Hessian, while the second diagonal matrix is chosen so as to induce positive definiteness of the diagonal approximation at a whole. Some numerical results are also presented to illustrate the effectiveness of our approximating matrices when incorporated within the L-BFGS algorithm. [ABSTRACT FROM AUTHOR]

This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just On. Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods. [ABSTRACT FROM AUTHOR]

The present paper describes a parallel preconditioned algorithm for the solution of partial eigenvalue problems for large sparse symmetric matrices, on parallel computers. Namely, we consider the Deflation-Accelerated Conjugate Gradient (DACG) algorithm accelerated by factorized-sparse- approximate-inverse- (FSAI-) type preconditioners. We present an enhanced parallel implementation of the FSAI preconditioner and make use of the recently developed Block FSAI-IC preconditioner, which combines the FSAI and the Block Jacobi-IC preconditioners. Results onto matrices of large size arising from finite element discretization of geomechanical models reveal that DACG accelerated by these type of preconditioners is competitive with respect to the available public parallel hypre package, especially in the computation of a few of the leftmost eigenpairs. The parallel DACG code accelerated by FSAI is written in MPI-Fortran 90 language and exhibits good scalability up to one thousand processors. [ABSTRACT FROM AUTHOR]

This paper deals with an inverse problem for identifying multiparameters in 1D space fractional advection dispersion equation (FADE) on a finite domain with final observations. The parameters to be identified are the fractional order, the diffusion coefficient, and the average velocity in the FADE. The forward problem is solved by a finite difference scheme, and then an optimal perturbation regularization algorithm is introduced to determine the three parameters simultaneously. Numerical inversions are performed both with the accurate data and noisy data, and several factors having influences on realization of the algorithm are discussed. The inversion solutions are in good approximations to the exact solutions demonstrating the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Under the condition that the values of mapping F are evaluated approximately, we propose a proximal analytic center cutting plane algorithm for solving variational inequalities. It can be considered as an approximation of the earlier cutting plane method, and the conditions we impose on the corresponding mappings are more relaxed. The convergence analysis for the proposed algorithm is also given at the end of this paper. [ABSTRACT FROM AUTHOR]

Very recently, Ahmad and Yao 2009( introduced and considered a system of generalized resolvent equationswith corresponding system of variational inclusions in uniformly smooth Banach spaces. In this paper we introduce and study a general system of generalized resolvent equations with corresponding general system of variational inclusions in uniformly smooth Banach spaces. We establish an equivalence relation between general system of generalized resolvent equations and general system of variational inclusions. The iterative algorithms for finding the approximate solutions of general system of generalized resolvent equations are proposed. The convergence criteria of approximate solutions of general system of generalized resolvent equations obtained by the proposed iterative algorithm are also presented. Our results represent the generalization, improvement, supplement, and development of Ahmad and Yao corresponding ones. [ABSTRACT FROM AUTHOR]

Very recently, Moudafi (2011) introduced an algorithm with weak convergence for the split common fixed-point problem. In this paper, we will continue to consider the split common fixedpoint problem. We discuss the strong convergence of the viscosity approximation method for solving the split common fixed-point problem for the class of quasi-nonexpansive mappings in Hilbert spaces. Our results improve and extend the corresponding results announced by many others. [ABSTRACT FROM AUTHOR]

Convex multiobjective programming problems and multiplicative programming problems have important applications in areas such as finance, economics, bond portfolio optimization, engineering, and other fields. This paper presents a quite easy algorithm for generating a number of efficient outcome solutions for convex multiobjective programming problems. As an application, we propose an outer approximation algorithm in the outcome space for solving the multiplicative convex program. The computational results are provided on several test problems. [ABSTRACT FROM AUTHOR]