University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
1
2017
06
01
GGMRES: A GMRES--type algorithm for solving singular linear equations with index one
1
14
EN
Alireza
Ataei
Mathematics Department, Faculty of Science, Persian Gulf University, Iran
ataei@pgu.ac.ir
Faezeh
Toutounian
Department of Applied Mathematics, School of Mathematical Sciences
toutouni@math.um.ac.ir
10.22124/jmm.2017.1954
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.
singular linear systems,DGMRES method,group-inverse solution,Drazin-inverse solution,Krylov subspace methods
http://jmm.guilan.ac.ir/article_1954.html
http://jmm.guilan.ac.ir/article_1954_dcd4f79f7ead59a08d2173d1dbddaad0.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
1
2017
06
01
Robust portfolio selection with polyhedral ambiguous inputs
15
26
EN
Somayyeh
Lotfi
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
slotfi@phd.guilan.ac.ir
Maziar
Salahi
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
salahim@guilan.ac.ir
Farshid
Mehrdoust
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
fmehrdoust@guilan.ac.ir
10.22124/jmm.2017.2004
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.
data ambiguity,conditional value-at-risk,polyhedral ambiguity set,robust optimization
http://jmm.guilan.ac.ir/article_2004.html
http://jmm.guilan.ac.ir/article_2004_1d74d05dba0e222372683aab00dd663c.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
1
2017
06
01
A numerical method for solving nonlinear partial differential equations based on Sinc-Galerkin method
27
40
EN
Ali
Zakeri
Faculty of Mathematical Sciences, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
azakeri@kntu.ac.ir
Amir Hossein
Salehi Shayegan
Faculty of Mathematical Sciences, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
ah.salehi@mail.kntu.ac.ir
Fatemeh
Asadollahi
Faculty of Mathematical Sciences, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
f.asadollahi@sina.kntu.ac.ir
10.22124/jmm.2017.2079
In this paper, we consider two dimensional nonlinear elliptic equations of the form $ -{rm div}(a(u,nabla 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.
Sinc-Galerkin method,elliptic partial differential equations,nonlinear problems,numerical solutions
http://jmm.guilan.ac.ir/article_2079.html
http://jmm.guilan.ac.ir/article_2079_9ed41d4df0353ca9b00dafbb90cd4c8c.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
1
2017
06
01
Mixed two-stage derivative estimator for sensitivity analysis
41
52
EN
Kolsoom
Mirabi
Department of Statistics, School of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
g.mirabi66@yahoo.com
Mohammad
Arashi
Department of Statistics, School of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
m_arashi_stat@yahoo.com
10.22124/jmm.2017.2211
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.
derivative estimator,infinitesimal perturbation analysis,measure-valued,risk analysis,score function,stochastic activity network
http://jmm.guilan.ac.ir/article_2211.html
http://jmm.guilan.ac.ir/article_2211_654dd56a77eaa7c5441494a27081eb41.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
1
2017
06
01
Determining optimal value of the shape parameter $c$ in RBF for unequal distances topographical points by Cross-Validation algorithm
53
60
EN
Mohammadreza
Yaghouti
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
yaghouti@guilan.ac.ir
Habibe
Ramezannezhad Azarboni
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
heral_ramezannezhad@yahoo.com
10.22124/jmm.2017.2225
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.
Radial Basis Function,Cross-Validation error,three-dimensional image
http://jmm.guilan.ac.ir/article_2225.html
http://jmm.guilan.ac.ir/article_2225_aa76072c0b4d04bfa157f4f964478609.pdf
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
5
1
2017
06
01
A numerical approach to solve eighth order boundary value problems by Haar wavelet collocation method
61
75
EN
Arikera Padmanabha
Reddy
Department of Mathematics, V. S. K. University, Ballari, India
paddu.padmanabha@gmail.com
Manjula
Harageri
Department of Mathematics, V. S. K. University, Ballari, India
manjulaharageri@gmail.com
Channaveerapala
Sateesha
Department of Mathematics, V. S. K. University, Ballari, India
csatish9980@gmail.com
10.22124/jmm.2017.2296
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.
Haar wavelet,Eighth order boundary value problems,collocation method
http://jmm.guilan.ac.ir/article_2296.html
http://jmm.guilan.ac.ir/article_2296_a101cfd2f23c799df5988bdb40444a02.pdf