As we know the approximation solution of seventh order two points boundary value problems based on B-spline of degree eight has only ${cal O}(h^{2})$ accuracy and this approximation is non-optimal. In this work, we obtain an optimal spline collocation method for solving the general nonlinear seventh order two points boundary value problems. The ${cal O}(h^{8})$ convergence analysis, mainly base...

It is firstly proved that the multi-input-single-output (MISO) fuzzy systems based on interval-valued $R$- and $S$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  A formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

      In this article, the crystallization of polyethylene is investigated by the modified weighted density approximation. Also, a direct correlation function of polyethylene based on the RISM theory is used. The free energy of a polyethylene is calculated using the density functional theory. The crystallization and also the solid and liquid densities of polyethylene are calculated and compared...

Temporal difference (TD) learning is a model-free reinforcement learning technique, which adopts an infinite horizon discount model and uses an incremental learning technique for dynamic programming. The state value function is updated in terms of sample episodes. Utilising eligibility traces is a key mechanism in enhancing the rate of convergence. TD(λ) represents the use of eligibility traces...

This paper investigates the performances of artificial neural networks approximation, the Translog and the Fourier flexible functional forms for the cost function, when different production technologies are used. Using simulated data bases, the author provides a comparison in terms of capability to reproduce input demands and in terms of the corresponding input elasticities of substitution esti...

Surrogate assisted evolutionary algorithms (EA) are rapidly gaining popularity where applications of EA in complex real world problem domains are concerned. Although EAs are powerful global optimizers, finding optimal solution to complex high dimensional, multimodal problems often require very expensive fitness function evaluations. Needless to say, this could brand any population-based iterati...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

Randomization is a fundamental tool used in many theoretical and practical areas of computer science. We study here the role of randomization in the area of submodular function maximization. In this area most algorithms are randomized, and in almost all cases the approximation ratios obtained by current randomized algorithms are superior to the best results obtained by known deterministic algor...

We propose a new method called C-SOM for function approximation. C-SOM extends the standard Self-Organizing Map (SOM) with a combination of Local Linear Mapping (LLM) and cubic spline based interpolation techniques to improve standard SOMs' generalization capabilities. CSOM uses the gradient information provided by the LLM technique to compute a cubic spline interpolation in the input space bet...

1. Abstract We propose a reliability analysis (RA) method that obtains the probability of failure by sequentially approximating the cumulative distribution function (CDF). This method uses the concept of the first order reliability method (FORM) in estimating the probability of failure but does not solve the optimization problem to obtain the most probable point (MPP). The goal of the proposed ...