eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-06-01
5
1
1
14
10.22124/jmm.2017.1954
1954
مقاله پژوهشی
GGMRES: A GMRES--type algorithm for solving singular linear equations with index one
Alireza Ataei
ataei@pgu.ac.ir
1
Faezeh Toutounian
toutouni@math.um.ac.ir
2
Mathematics Department, Faculty of Science, Persian Gulf University, Iran
Department of Applied Mathematics, School of Mathematical Sciences
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.
https://jmm.guilan.ac.ir/article_1954_dcd4f79f7ead59a08d2173d1dbddaad0.pdf
singular linear systems
DGMRES method
group-inverse solution
Drazin-inverse solution
Krylov subspace methods
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-06-01
5
1
15
26
10.22124/jmm.2017.2004
2004
مقاله پژوهشی
Robust portfolio selection with polyhedral ambiguous inputs
Somayyeh Lotfi
slotfi@phd.guilan.ac.ir
1
Maziar Salahi
salahim@guilan.ac.ir
2
Farshid Mehrdoust
fmehrdoust@guilan.ac.ir
3
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
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.
https://jmm.guilan.ac.ir/article_2004_1d74d05dba0e222372683aab00dd663c.pdf
data ambiguity
conditional value-at-risk
polyhedral ambiguity set
robust optimization
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-06-01
5
1
27
40
10.22124/jmm.2017.2079
2079
مقاله پژوهشی
A numerical method for solving nonlinear partial differential equations based on Sinc-Galerkin method
Ali Zakeri
azakeri@kntu.ac.ir
1
Amir Hossein Salehi Shayegan
ah.salehi@mail.kntu.ac.ir
2
Fatemeh Asadollahi
f.asadollahi@sina.kntu.ac.ir
3
Faculty of Mathematical Sciences, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
Faculty of Mathematical Sciences, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
Faculty of Mathematical Sciences, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran
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.
https://jmm.guilan.ac.ir/article_2079_9ed41d4df0353ca9b00dafbb90cd4c8c.pdf
Sinc-Galerkin method
elliptic partial differential equations
nonlinear problems
numerical solutions
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-06-01
5
1
41
52
10.22124/jmm.2017.2211
2211
مقاله پژوهشی
Mixed two-stage derivative estimator for sensitivity analysis
Kolsoom Mirabi
g.mirabi66@yahoo.com
1
Mohammad Arashi
m_arashi_stat@yahoo.com
2
Department of Statistics, School of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
Department of Statistics, School of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran
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.
https://jmm.guilan.ac.ir/article_2211_654dd56a77eaa7c5441494a27081eb41.pdf
derivative estimator
infinitesimal perturbation analysis
measure-valued
risk analysis
score function
stochastic activity network
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-06-01
5
1
53
60
10.22124/jmm.2017.2225
2225
مقاله پژوهشی
Determining optimal value of the shape parameter $c$ in RBF for unequal distances topographical points by Cross-Validation algorithm
Mohammadreza Yaghouti
yaghouti@guilan.ac.ir
1
Habibe Ramezannezhad Azarboni
heral_ramezannezhad@yahoo.com
2
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran
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.
https://jmm.guilan.ac.ir/article_2225_aa76072c0b4d04bfa157f4f964478609.pdf
Radial Basis Function
Cross-Validation error
three-dimensional image
eng
University of Guilan
Journal of Mathematical Modeling
2345-394X
2382-9869
2017-06-01
5
1
61
75
10.22124/jmm.2017.2296
2296
مقاله پژوهشی
A numerical approach to solve eighth order boundary value problems by Haar wavelet collocation method
Arikera Padmanabha Reddy
paddu.padmanabha@gmail.com
1
Manjula Harageri
manjulaharageri@gmail.com
2
Channaveerapala Sateesha
csatish9980@gmail.com
3
Department of Mathematics, V. S. K. University, Ballari, India
Department of Mathematics, V. S. K. University, Ballari, India
Department of Mathematics, V. S. K. University, Ballari, India
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.
https://jmm.guilan.ac.ir/article_2296_a101cfd2f23c799df5988bdb40444a02.pdf
Haar wavelet
Eighth order boundary value problems
collocation method