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Published in: Soft Computing 2/2020

19-04-2019 | Methodologies and Application

Monte Carlo method for the real and complex fuzzy system of linear algebraic equations

Authors: Behrouz Fathi-Vajargah, Zeinab Hassanzadeh

Published in: Soft Computing | Issue 2/2020

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Abstract

In this paper, we apply the Monte Carlo method to solve the real and complex fuzzy system of linear algebraic equations via new techniques. At first, we determine the specified and simpler computing condition for convergence of the Monte Carlo method using Hadamard product related to select the transition probability matrix. Then, we employ the new strategy based on the exclusive characteristic of the Monte Carlo method to find the solution of the real and complex fuzzy system of linear algebraic equations. Finally, some numerical examples are proposed to demonstrate the validity and efficiency of the discussed theoretical concepts.

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Literature
go back to reference Allahviranloo T (2004) Numerical methods for fuzzy system of linear equations. Appl Math Comput 155(2):493–502MathSciNetMATH Allahviranloo T (2004) Numerical methods for fuzzy system of linear equations. Appl Math Comput 155(2):493–502MathSciNetMATH
go back to reference Allahviranloo T, Salahshour S (2011) Fuzzy symmetric solutions of fuzzy linear systems. Comput Appl Math 235(16):4545–4553MathSciNetMATH Allahviranloo T, Salahshour S (2011) Fuzzy symmetric solutions of fuzzy linear systems. Comput Appl Math 235(16):4545–4553MathSciNetMATH
go back to reference Axelsson O (1996) Iterative solution methods. Cambridge University Press, CambridgeMATH Axelsson O (1996) Iterative solution methods. Cambridge University Press, CambridgeMATH
go back to reference Axelsson O, Neytcheva M, Ahmad B (2014) A comparison of iterative methods to solve complex valued linear algebraic systems. Numer Algorithms 66(4):811–841MathSciNetMATH Axelsson O, Neytcheva M, Ahmad B (2014) A comparison of iterative methods to solve complex valued linear algebraic systems. Numer Algorithms 66(4):811–841MathSciNetMATH
go back to reference Behera D, Chakraverty S (2012) A new method for solving real and complex fuzzy systems of linear equations. Comput Math Model 23(4):507–518MathSciNetMATH Behera D, Chakraverty S (2012) A new method for solving real and complex fuzzy systems of linear equations. Comput Math Model 23(4):507–518MathSciNetMATH
go back to reference Behera D, Chakraverty S (2013) Fuzzy center based solution of fuzzy complex linear system of equations. Int J Uncertain Fuzziness Knowl Based Syst 21(4):629–642MATH Behera D, Chakraverty S (2013) Fuzzy center based solution of fuzzy complex linear system of equations. Int J Uncertain Fuzziness Knowl Based Syst 21(4):629–642MATH
go back to reference Behera D, Chakraverty S (2014) Solving fuzzy complex system of linear equations. Inf Sci 277(1):154–162MathSciNetMATH Behera D, Chakraverty S (2014) Solving fuzzy complex system of linear equations. Inf Sci 277(1):154–162MathSciNetMATH
go back to reference Benzi M, Bertaccini D (2008) Block preconditioning of real-valued iterative algorithms for complex linear systems. IMA J Numer Anal 28(3):598–618MathSciNetMATH Benzi M, Bertaccini D (2008) Block preconditioning of real-valued iterative algorithms for complex linear systems. IMA J Numer Anal 28(3):598–618MathSciNetMATH
go back to reference Berman A, Plemmons R (1994) Nonnegative matrices in the mathematical sciences. SIAM, PhiladelphiaMATH Berman A, Plemmons R (1994) Nonnegative matrices in the mathematical sciences. SIAM, PhiladelphiaMATH
go back to reference Branford S, Sahin C, Thandavan A, Weihrauch C, Alexandrov V, Dimov IT (2008) Monte Carlo methods for matrix computations on the grid. Future Gener Comput Syst 24(6):605–612 Branford S, Sahin C, Thandavan A, Weihrauch C, Alexandrov V, Dimov IT (2008) Monte Carlo methods for matrix computations on the grid. Future Gener Comput Syst 24(6):605–612
go back to reference Cheng G (2014) New bounds for eigenvalues of the Hadamard product and the Fan product of matrices. Taiwan J Math 18(1):305–312MathSciNetMATH Cheng G (2014) New bounds for eigenvalues of the Hadamard product and the Fan product of matrices. Taiwan J Math 18(1):305–312MathSciNetMATH
go back to reference Cheng G, Rao X (2013) Some inequalities for the spectral radius of the Hadamard product of two nonnegative matrices. J Math Inequal 7(3):529–534MathSciNetMATH Cheng G, Rao X (2013) Some inequalities for the spectral radius of the Hadamard product of two nonnegative matrices. J Math Inequal 7(3):529–534MathSciNetMATH
go back to reference Day D, Heroux AM (2001) Solving complex-valued linear systems via equivalent real formulations. SIAM J Sci Comput 23(2):480–498MathSciNetMATH Day D, Heroux AM (2001) Solving complex-valued linear systems via equivalent real formulations. SIAM J Sci Comput 23(2):480–498MathSciNetMATH
go back to reference Dehghan D, Hashemi B (2006) Iterative solution of fuzzy linear systems. Appl Math Comput 175(1):645–674MathSciNetMATH Dehghan D, Hashemi B (2006) Iterative solution of fuzzy linear systems. Appl Math Comput 175(1):645–674MathSciNetMATH
go back to reference Dimov I, Maire S, Sellier JM (2015) A new walk on equations Monte Carlo method for solving systems of linear algebraic equations. Appl Math Model 39(15):4494–4510MathSciNetMATH Dimov I, Maire S, Sellier JM (2015) A new walk on equations Monte Carlo method for solving systems of linear algebraic equations. Appl Math Model 39(15):4494–4510MathSciNetMATH
go back to reference Fang M (2007) Bounds on eigenvalues of the Hadamard product and the Fan product of matrices. Linear Algebra Appl 425(1):7–15MathSciNetMATH Fang M (2007) Bounds on eigenvalues of the Hadamard product and the Fan product of matrices. Linear Algebra Appl 425(1):7–15MathSciNetMATH
go back to reference Fathi-Vajargah B, Hassanzadeh Z (2018) Improvements on the hybrid Monte Carlo algorithms for matrix computations. Sādhanā 44(1):1–13MathSciNet Fathi-Vajargah B, Hassanzadeh Z (2018) Improvements on the hybrid Monte Carlo algorithms for matrix computations. Sādhanā 44(1):1–13MathSciNet
go back to reference Guo QP, Li HB, Song MY (2013) New inequalities on eigenvalues of the Hadamard product and the Fan product of matrices. J Inequal Appl 2013(1):421–433MathSciNetMATH Guo QP, Li HB, Song MY (2013) New inequalities on eigenvalues of the Hadamard product and the Fan product of matrices. J Inequal Appl 2013(1):421–433MathSciNetMATH
go back to reference Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, CambridgeMATH Horn RA, Johnson CR (1985) Matrix analysis. Cambridge University Press, CambridgeMATH
go back to reference Horn RA, Johnson CR (1991) Topics in matrix analysis. Cambridge University Press, New YorkMATH Horn RA, Johnson CR (1991) Topics in matrix analysis. Cambridge University Press, New YorkMATH
go back to reference Horn RA, Zhang F (2010) Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefinite matrices. Electron J Linear Algebra 20(1):90–94MathSciNetMATH Horn RA, Zhang F (2010) Bounds on the spectral radius of a Hadamard product of nonnegative or positive semidefinite matrices. Electron J Linear Algebra 20(1):90–94MathSciNetMATH
go back to reference Ji H, Mascagni M, Li Y (2013) Convergence analysis of Markov chain Monte Carlo linear solvers using Ulam-Von Neumann algorithm. SIAM J Numer Anal 51(4):2107–2122MathSciNetMATH Ji H, Mascagni M, Li Y (2013) Convergence analysis of Markov chain Monte Carlo linear solvers using Ulam-Von Neumann algorithm. SIAM J Numer Anal 51(4):2107–2122MathSciNetMATH
go back to reference Liu Q, Chen G (2009) On two inequalities for the Hadamard product and the Fan product of matrices. Linear Algebra Appl 431(5):974–984MathSciNetMATH Liu Q, Chen G (2009) On two inequalities for the Hadamard product and the Fan product of matrices. Linear Algebra Appl 431(5):974–984MathSciNetMATH
go back to reference Majumdar S (2013) Numerical solutions of fuzzy complex system of linear equations. German J Adv Math Sci 1(1):20–26 Majumdar S (2013) Numerical solutions of fuzzy complex system of linear equations. German J Adv Math Sci 1(1):20–26
go back to reference Rahgooy T, Yazdi HS, Monsefi R (2009) Fuzzy complex system of linear equations applied to circuit analysis. Int J Comput Electr Eng 1(5):535–541 Rahgooy T, Yazdi HS, Monsefi R (2009) Fuzzy complex system of linear equations applied to circuit analysis. Int J Comput Electr Eng 1(5):535–541
go back to reference Saad Y (2003) Iterative methods for sparse linear systems. SIAMY, PhiladelphiaMATH Saad Y (2003) Iterative methods for sparse linear systems. SIAMY, PhiladelphiaMATH
go back to reference Salkuyeh DK (2015) On the solution of a class of fuzzy system of linear equations. Sādhanā 40(2):369–377MathSciNet Salkuyeh DK (2015) On the solution of a class of fuzzy system of linear equations. Sādhanā 40(2):369–377MathSciNet
go back to reference Tamir DE, Rishe ND, Kandel A (2015) Complex fuzzy sets and complex fuzzy logic an overview of theory and applications. Stud Fuzziness Soft Comput 326(1):661–681MathSciNetMATH Tamir DE, Rishe ND, Kandel A (2015) Complex fuzzy sets and complex fuzzy logic an overview of theory and applications. Stud Fuzziness Soft Comput 326(1):661–681MathSciNetMATH
Metadata
Title
Monte Carlo method for the real and complex fuzzy system of linear algebraic equations
Authors
Behrouz Fathi-Vajargah
Zeinab Hassanzadeh
Publication date
19-04-2019
Publisher
Springer Berlin Heidelberg
Published in
Soft Computing / Issue 2/2020
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-019-03960-1

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