Shahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601Tensor LU and QR decompositions and their randomized algorithms11610197810.52547/CMCMA.1.1.1ENYuefeng ZhuSchool of Mathematical Sciences, Fudan University, Shanghai, P.R. ChinaYimin WeiSchool of Mathematical Sciences and Shanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai, PR ChinaJournal Article20211210In this paper, we propose two decompositions extended from matrices to tensors, including LU and QR decompositions with their rank-revealing and randomized variations. We give the growth order analysis of error of the tensor QR (t-QR) and tensor LU (t-LU) decompositions. Growth order of error and running time are shown by numerical examples. We test our methods by compressing and analyzing the image-based data, showing that the performance of tensor randomized QR decomposition is better than the tensor randomized SVD (t-rSVD) in terms of the accuracy, running time and memory.https://cmcma.sbu.ac.ir/article_101978_439808673027f89a058c53eb908c4262.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601From symplectic eigenvalues of positive definite matrices to their pseudo-orthogonal eigenvalues172010199110.52547/CMCMA.1.1.17ENKh.D. IkramovaMoscow Lomonosov State University, Moscow, RussiaAlimohammad NazariJournal Article20211223Williamson's theorem states that every real symmetric positive definite matrix $A$ of even order can be brought to diagonal form via a symplectic $T$-congruence transformation. The diagonal entries of the resulting diagonal form are called the symplectic eigenvalues of $A$. We point at an analog of this classical result related to Hermitian positive definite matrices, *-congruences, and another class of transformation matrices, namely, pseudo-unitary matrices. This leads to the concept of pseudo-unitary (or pseudo-orthogonal, in the real case) eigenvalues of positive definite matrices.https://cmcma.sbu.ac.ir/article_101991_930629420cb285a6a38484522f0c0cdd.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601Solving parameterized generalized inverse eigenvalue problems via Golub-Kahan bidiagonalization213610199210.52547/CMCMA.1.1.21ENZeynab DalvandDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran0000-0002-6527-9458Mohammad Ebrahim DastyarDepartment of Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran0000-0003-3423-7869Journal Article20211213In this study, we present two two-step methods to solve parameterized generalized inverse eigenvalue problems that appear in diverse areas of computation and engineering applications. At the first step, we transfer the inverse eigenvalue problem into a system of nonlinear equations by using of the Golub-Kahan bidiagonalization. At the second step, we use Newton's and Quasi-Newton's methods for the numerical solution of system of nonlinear equations. Finally, we present some numerical examples which show that our methods are applicable for solving the parameterized inverse eigenvalue problems.https://cmcma.sbu.ac.ir/article_101992_75a1235cf3c0015c32d00147235f417f.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601On rank decomposition and semi-symmetric rank decomposition of semi-symmetric tensors374710199310.52547/CMCMA.1.1.37ENHassan BozorgmaneshDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Shahid Beheshti University, Tehran, IranAnthony TheodoreChronopoulosDepartment of Computer Science, University of Texas, San Antonio, Texas
78249, USA.
(Visiting Faculty) Department of Computer Engineering & Informatics, University of
Patras, Rio 26500, Greece.Journal Article20211124A tensor is called semi-symmetric if all modes but one, are symmetric. In this paper, we study the CP decomposition of semi-symmetric tensors or higher-order individual difference scaling (INDSCAL). Comon's conjecture states that for any symmetric tensor, the CP rank and symmetric CP rank are equal, while it is known that Comon's conjecture is not true in the general case but it is proved under several assumptions in the literature. In the paper, Comon's conjecture is extended for semi-symmetric CP decomposition and CP decomposition of semi-symmetric tensors under suitable assumptions. Specially, we show that if a semi-symmetric tensor has a CP rank smaller or equal to its order, or when the semi-symmetric CP rank is less than/or equal to the dimension, then the semi-symmetric CP rank is equal to the CP rank.https://cmcma.sbu.ac.ir/article_101993_3d209bbe504397a58dee9c25066bf2da.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601Comparing image segmentation methods using data envelopment analysis485510203910.52547/CMCMA.1.1.48ENHassan BozorgmaneshDepartment of Applied Mathematics, Faculty of Mathematical Sciences,
Shahid Beheshti University, Tehran, IranJournal Article20211222In this paper, a model based on data envelopment analysis is used for comparing di erent image segmentation methods<br />and also for the purpose of nding the best parameter among certain values for a method. The criteria for choosing inputs<br />and outputs are explained and in the end, some examples are presented to demonstrate how this model works.https://cmcma.sbu.ac.ir/article_102039_fb0ab977c4944607ca48da27b25ca583.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601Ball comparison between three fourth convergence order schemes for nonlinear equations566210208910.52547/CMCMA.1.1.56ENSamundra RegmiLearning Commons, University of North Texas at Dallas, Dallas, TX, USAIoannis Konstantinos ArgyrosDepartment of Mathematical Sciences, Cameron University, Lawton, OK 73505, USASanthosh GeorgeDepartment of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India-575 025Christopher I.ArgyrosDepartment of Computing and Technology, Cameron University, Lawton, OK 73505, USAJournal Article20220118A ball convergence comparison is developed between three Banach space valued schemes of fourth convergence order to solve nonlinear models under $\omega-$continuity conditions on the derivative.https://cmcma.sbu.ac.ir/article_102089_cf4d024e6ae9b38219b60bf30a4c96cf.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601On the semi-local convergence of the Homeier method in Banach space for solving equations636810224710.52547/CMCMA.1.1.63ENSamundra RegmiLearning Commons, University of North Texas at Dallas, Dallas, TX, USAIoannis Konstantinos ArgyrosDepartment of Mathematical Sciences, Cameron University, Lawton, OK 73505, USASanthosh GeorgeDepartment of Mathematical and Computational Sciences,National Institute of Technology Karnataka, India-575 025Christopher I.ArgyrosDepartment of Computing and Technology, Cameron University, Lawton, OK 73505, USAJournal Article20220215In this paper we consider the semi-local convergence analysis of the Homeier method for solving nonlinear equation in Banach space. As far as we know no semi-local convergence has been given for the Homeier under Lipschitz conditions. Our goal is to extend the applicability of the Homeier method in the semi-local convergence under these conditions. We use majorizing sequences and conditions only on the first derivative which appear on the method for proving our results. Numerical experiments are provided in this study.https://cmcma.sbu.ac.ir/article_102247_8701bc381ac4a92846c5678cb29dcc55.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601Numerical solution of differential equations of Lane-Emden type by Gegenbauer and rational Gegenbauer collocation methods698510363210.52547/CMCMA.1.1.69ENFatemeh BaharifardSchool of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran0000-0002-3391-4461Kourosh ParandDepartment of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran0000-0001-5946-0771Journal Article20230512In this paper, we apply the collocation method for solving some classes of Lane-Emden type equations that are determined in interval $[0, 1]$ and semi-infinite domain. We use an orthogonal system of functions, namely Gegenbauer polynomials and introduce the shifted Gegenbauer polynomials and the rational Gegenbauer functions as basis functions in the collocation method for problems in interval $[0, 1]$ and semi-infinite domain, respectively.<br />We estimate that the proposed method has super-linear convergence rate<br />and also investigate the Gegenbauer parameter $ (\alpha)$ to get more accurate answers for various Lane-Emden type problems. The comparison between the proposed method and other numerical results shows that the method is efficient and applicable. https://cmcma.sbu.ac.ir/article_103632_ade139c3cdde52688a0180edfe593818.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601Hermite neural network for solving the Blasius equation869410363310.52547/CMCMA.1.1.86ENAida PakniyatDepartment of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, IranKourosh ParandDepartment of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran0000-0001-5946-0771Journal Article20230509In this paper, we propose a Hermite neural network method for solving the Blasius equation, a nonlinear ordinary differential equation defined on the semi-infinite interval. In this work, Hermite functions are transformed using variable transformation in a semi-infinite domain. Hermite functions are used for the first time in a neural network to solve Blasius differential equations, making this method better than existing networks. This method is efficient for solving differential equations. In this paper, we explore the benefits of using the backpropagation algorithm to update parameters for neural networks. By applying this approach, we can successfully avoid issues such as overflow and local minima, which are common challenges associated with other optimization methods. The results obtained are compared with other methods to validate the proposed method and presented in both graphical and tabular form.https://cmcma.sbu.ac.ir/article_103633_7cbab4addf92e594949f0e55ab2af319.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601A distributed approach for a COVID-19 fractional time-delay model9510410365110.52547/CMCMA.1.1.95ENMahdi Movahedian MoghaddamDepartment of Computer and Data Sciences, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran0000-0002-6513-5251Journal Article20230327After the spread of COVID-19, several attempts were made to model it mathematically. Due to the high power of fractional differential equation modeling, a time delay fractional model was presented for the modeling spread of COVID-19. The solution of these models is done by computer systems in several ways, including the fractional predictor-corrector method, which has many challenges. Among these challenges are execution time, scalability, and memory consumption. In previous research, the shared memory approach was presented to reduce the execution time challenge. Still, because of the challenges of scalability and memory consumption, a coarse-grained distributed approach was presented in this research. The results presented in this research have been compared with sequential approaches and shared memory. These results have been implemented based on the data announced by the city of Wuhan in 2019, and a speedup of 1.704 was achieved per execution on 1000 inputshttps://cmcma.sbu.ac.ir/article_103651_a5a4b86f1863cc5c6951777296c93fa5.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601Solving linear systems of equations by two-step diagonal and off-diagonal multisplitting methods10511510372910.52547/CMCMA.1.1.105ENMaryam BashirizadehDepartment of Applied Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran.0009-0004-6520-2700Journal Article20230514In the realm of solving large linear systems of equations, multisplitting methods emerge as a prominent class of iterative techniques. This paper introduces two-step diagonal and off-diagonal multisplitting methods and evaluates their effectiveness in comparison to symmetric successive overrelaxation multisplitting and quasi-Chebyshev accelerated multisplitting techniques for solving linear systems of equations. Additionally, this study investigates convergence theorems when the system matrix is an $H$-matrix and demonstrates the effectiveness of the proposed methods by presenting numerical results.https://cmcma.sbu.ac.ir/article_103729_1d5dd83c5fe18e5393393c99118885d7.pdfShahid Beheshti UniversityComputational Mathematics and Computer Modeling with Applications (CMCMA)2783-48591120220601A comparison between pre-Newton and post-Newton approaches for solving a physical singular second-order boundary problem in the semi-infinite interval11612510373010.52547/CMCMA.1.1.116ENAmir Hosein Hadian RasananSchool of Computer Science, Institute for Research in Fundamental Sciences (IPM), Tehran, IranMehran NikaryaDepartment of Electrical Engineering and Information Technology, Iranian Research Organization for Science and Technology (IROST), Tehran, IranMohammad Mahdi MoayeriDepartment of Computer and Data Sciences, Shahid Beheshti University, Tehran, Iran.Arman BahramnezhadDepartment of Computer and Data Sciences, Shahid Beheshti University, Tehran, IranJournal Article20221029In this paper, two numerical approaches based on the Newton iteration method with spectral algorithms are introduced to solve the Thomas-Fermi equation. That Thomas-Fermi equation is a nonlinear singular ordinary differential equation (ODE) with a boundary condition in infinite. In these schemes, the Newton method is combined with a spectral method where in one of those, by the Newton method we convert nonlinear ODE to a sequence of linear ODE and then, solve them using the spectral method. In another one, by the spectral method, the nonlinear ODE is converted to a system of nonlinear algebraic equations, then, this system is solved by the Newton method. In both approaches, the spectral method is based on the fractional order of rational Gegenbauer functions. Finally, the obtained results of the two introduced schemes are compared to each other in accuracy, runtime, and iteration number. Numerical experiments are presented showing that our methods are as accurate as the best results obtained until now.https://cmcma.sbu.ac.ir/article_103730_52acfa13c0dd4449bdf6b6929535fd51.pdf