Search

In this paper, we study a kind of conjugate gradient viscosity approximation algorithm for finding a common solution of split generalized equilibrium problem and variational inequality problem. Under mild conditions, we prove that the sequence generated by the proposed iterative algorithm converges strongly to the common solution. The conclusion presented in this paper is the generalization, extension, and supplement of the previously known results in the corresponding references. Some numerical results are illustrated to show the feasibility and efficiency of the proposed 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]

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]

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]

Adaptive neurofuzzy inference systems (ANFIS) represent an efficient technique for the solution of function approximation problems. When numerical samples are available in this regard, the synthesis of ANFIS networks can be carried out exploiting clustering algorithms. Starting from a hyperplane clustering synthesis in the joint input-output space, a computationally efficient optimization of ANFIS networks is proposed in this paper. It is based on a hierarchical constructive procedure, by which the number of rules is progressively increased and the optimal one is automatically determined on the basis of learning theory in order to maximize the generalization capability of the resulting ANFIS network. Extensive computer simulations prove the validity of the proposed algorithm and show a favorable comparison with other well-established techniques. [ABSTRACT FROM AUTHOR]

We introduce a gradient descent algorithm for bipartite ranking with general convex losses. The implementation of this algorithm is simple, and its generalization performance is investigated. Explicit learning rates are presented in terms of the suitable choices of the regularization parameter and the step size. The result fills the theoretical gap in learning rates for ranking problem with general convex losses. [ABSTRACT FROM AUTHOR]

An iterative algorithm is constructed to solve the generalized coupled Sylvester matrix equations (AXB - CYD,EXF - GYH) = (M,N), which includes Sylvester and Lyapunov matrix equations as special cases, over generalized reflexive matrices X and Y. When the matrix equations are consistent, for any initial generalized reflexive matrix pair [X₁, Y₁], the generalized reflexive solutions can be obtained by the iterative algorithm within finite iterative steps in the absence of round-off errors, and the least Frobenius norm generalized reflexive solutions can be obtained by choosing a special kind of initial matrix pair. The unique optimal approximation generalized reflexive solution pair [...,Ŷ] to a given matrix pair [X0, Y0] in Frobenius norm can be derived by finding the least-norm generalized reflexive solution pair [...,Ỹ] of a new corresponding generalized coupled Sylvester matrix equation pair ... where ... Several numerical examples are given to show the effectiveness of the presented iterative algorithm. [ABSTRACT FROM AUTHOR]