Search

In the present paper, we discuss the approximation properties of Durrmeyer-Stancu type variant of Jain operators with the modified forms of the Beta basis functions. We establish some direct results, which include the asymptotic formula, the error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct a King modification of these operators which preserves the test functions e0 and e1. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniform approximation of functions by Meyer-König and Zeller operators of max-product type in some weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity. [ABSTRACT FROM AUTHOR]

This paper considers the problem of approximating an integrable function by piecewise linear functions that keep the integral and positivity of the original function. [ABSTRACT FROM AUTHOR]

In this work, we generated more topologies based on similarity relation for an information system and we found lower and upper approximations. This paper discussed two approaches for determining accuracy with Yao's method and Pawlak's method of qualitative data. From both ideas, it is seen that due to the uncertainty and vagueness of qualitative data, we get many topologies on one or two attributes. We determined the accuracies by the new method; this method showed the difference between one or two attributes. This method is clarified by application. [ABSTRACT FROM AUTHOR]

Many familiar household objects (such as sausages) involve the maximization of a volume under geometric constraints. A flexible but inextensible membrane bounds a volume which is to be filled to capacity. In the case of the sausage, a full analytic solution is here provided. Other related but more difficult problems seem to demand approximate methods of solution. [ABSTRACT FROM AUTHOR]

In a stopped arrival queue the arrival process is switched off as soon as the available queue space is full and not switched on again until there is space in the queue. A simple approximation for GI/GI/1/N stopped arrival queues is developed and shown to be remarkably accurate in predicting throughput. Because a two-stage flow line is equivalent to a stopped arrival queue, the GI/GI/1/N stopped arrival queue can be used as the building block for approximating the performance of multistage flow lines where the service times at the stages have general distributions. Numerical tests of the throughput approximation show that it gives accurate throughput predictions, in spite of its simplicity and minimal computation requirements. [ABSTRACT FROM AUTHOR]

A scaled memoryless BFGS preconditioned conjugate gradient algorithm for solving unconstrained optimization problems is presented. The basic idea is to combine the scaled memoryless BFGS method and the preconditioning technique in the frame of the conjugate gradient method. The preconditioner, which is also a scaled memoryless BFGS matrix, is reset when the Beale-Powell restart criterion holds. The parameter scaling the gradient is selected as the spectral gradient. In very mild conditions, it is shown that, for strongly convex functions, the algorithm is globally convergent. Computational results for a set consisting of 750 unconstrained optimization test problems show that this new scaled conjugate gradient algorithm substantially outperforms the known conjugate gradient methods including the spectral conjugate gradient by Birgin and Martínez [Birgin, E. and Martínez, J.M., 2001, A spectral conjugate gradient method for unconstrained optimization. Applied Mathematics and Optimization, 43, 117-128], the conjugate gradient by Polak and Ribière [Polak, E. and Ribière, G., 1969, Note sur la convergence de méthodes de directions conjuguées. Revue Francaise Informat. Reserche Opérationnelle, 16, 35-43], as well as the most recent conjugate gradient method with guaranteed descent by Hager and Zhang [Hager, W.W. and Zhang, H., 2005, A new conjugate gradient method with guaranteed descent and an efficient line search. SIAM Journal on Optimization, 16, 170-192; Hager, W.W. and Zhang, H., 2004, CG-DESCENT, A conjugate gradient method with guaranteed descent ACM Transactions on Mathematical Software, 32, 113-137]. [ABSTRACT FROM AUTHOR]

Generally, global convergence of the conjugate gradient methods for unconstrained optimization problems needs Wolfe line search or strong Wolfe line search. In this article, we propose a cautious DY conjugate gradient method and prove that this method with Armijo line search converges globally if the objective function has Lipschitz continuous gradients. We also present some preliminary numerical results to show the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

The Morigati's greatest convex method is applied to obtain sharp distribution-free lower and upper bounds on the error in approximating the expected values of kth record statistics via inverse hazard functions. [ABSTRACT FROM AUTHOR]

It is well known that a wide range of impulse control problems are continuous, but not differentiable, with respect to intervention cost as it approaches zero. We show a similar non-C1 result, assuming that the problem and the value function are sufficiently regular. The result is that if the value function is locally C1 in the state variable, then it does not admit first order approximation wrt. the intervention cost. Our analysis also covers problems with reflection (i.e., vanishing impulse). [ABSTRACT FROM AUTHOR]