فهرست مطالب

Mathematical Modeling - Volume:5 Issue:1, 2017
  • Volume:5 Issue:1, 2017
  • تاریخ انتشار: 1396/04/20
  • تعداد عناوین: 6
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  • Alireza Ataei *, Faezeh Toutounian Pages 1-14
    In this paper, an algorithm based on the Drazin generalized conjugate residual (DGMRES) algorithm is proposed for computing the group-inverse solution of singular linear equations with index one. Numerical experiments show that the resulting group-inverse solution is reasonably accurate and its computation time is significantly less than that of group-inverse solution obtained by the DGMRES algorithm.
    Keywords: singular linear systems, DGMRES method, group-inverse solution, Drazin-inverse solution, Krylov subspace methods
  • Somayyeh Lotfi *, Maziar Salahi, Farshid Mehrdoust Pages 15-26
    Ambiguity in the inputs of the models is typical especially in portfolio selection problem where the true distribution of random variables is usually unknown. Here we use robust optimization approach to address the ambiguity in conditional-value-at-risk minimization model. We obtain explicit models of the robust conditional-value-at-risk minimization for polyhedral and correlated polyhedral ambiguity sets of the scenarios. The models are linear programs in the both cases. Using a portfolio of USA stock market, we apply the buy-and-hold strategy to evaluate the model's performance.
    We found that the robust models have almost the same out-of-sample performance, and outperform the nominal model. However, the robust model with correlated polyhedral results in more conservative solutions.
    Keywords: data ambiguity, conditional value-at-risk, polyhedral ambiguity set, robust optimization
  • Ali Zakeri *, Amir Hossein Salehi Shayegan, Fatemeh Asadollahi Pages 27-40
    In this paper, we consider two dimensional nonlinear elliptic equations of the form −div(a(u,∇u))=f . Then, in order to solve these equations on rectangular domains, we propose a numerical method based on Sinc-Galerkin method. Finally, the presented method is tested on some examples. Numerical results show the accuracy and reliability of the proposed method.
    Keywords: Sinc-Galerkin method, elliptic partial differential equations, nonlinear problems, numerical solutions
  • Kolsoom Mirabi, Mohammad Arashi * Pages 41-52
    In mathematical modeling, determining most influential parameters on outputs is of major importance. Thus, sensitivity analysis of parameters plays an important role in model validation. We give detailed procedure of constructing a new derivative estimator for general performance measure in Gaussian systems. We will take advantage of using score function and measure-value derivative estimators in our approach. It is shown that the proposed estimator performs better than other estimators for a dense class of test functions in the sense of having smaller variance.
    Keywords: derivative estimator, infinitesimal perturbation analysis, measure-valued, risk analysis, score function, stochastic activity network
  • Mohammadreza Yaghouti *, Habibe Ramezannezhad Azarboni Pages 53-60
    Several radial basis function based methods contain a free shape parameter which has a crucial role in the accuracy of the methods. Performance evaluation of this parameter in different functions with various data has always been a topic of study. In the present paper, we consider studying the methods which determine an optimal value for the shape parameter in interpolations of radial basis functions for data collections produced by topographical images that are not necessarily in equal distances. The Cross-Validation method is picked out of several existing algorithms proposed for determining the shape parameter.
    Keywords: Radial Basis Function, Cross-Validation error, three-dimensional image
  • Arikera Padmanabha Reddy *, Manjula Harageri, Channaveerapala Sateesha Pages 61-75
    In this paper a robust and accurate algorithm based on Haar wavelet collocation method (HWCM) is proposed for solving eighth order boundary value problems. We used the Haar direct method for calculating multiple integrals of Haar functions. To illustrate the efficiency and accuracy of the concerned method, few examples are considered which arise in the mathematical modeling of fluid dynamics and hydromagnetic stability. Convergence and error bound estimation of the method are discussed. The comparison of results with exact solution and existing numerical methods such as Quintic B-spline collocation method and Galerkin method with Quintic B-splines as basis functions shown that the HWCM is a powerful numerical method for solution of above mentioned problems.
    Keywords: Haar wavelet, Eighth order boundary value problems, Collocation method