Abstract
In this Chapter methods are developed for numerical solution of system of linear equations through taking advantages of the properties of repetitive tridiagonal matrices. A system of linear equations is usually obtained in the final step of many science and engineering problems such as problems involving partial differential equations. In the proposed solutions, the problem is first solved for repetitive tridiagonal matrices and a closed-from relationship is obtained. This relationship is then utilized for the solution of a general matrix through converting the matrix into a repetitive tridiagonal matrix and the remaining matrix.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Shojaei, I., Rahami, H.: A new numerical solution for linear system of equations. Appl Math Comput, Submitted for Publication (2020)
Tian, Zh, Tian, M., Zhang, Y., Wen, P.: An iteration method for solving the linear system Ax = b. Comput. Math Appl. 75(8), 2710–2722 (2018)
Pratapa, PhP, Suryanarayana, Ph, Pask, J.E.: Anderson acceleration of the Jacobi iterative method: an efficient alternative to Krylov methods for large, sparse linear systems. J. Comput. Phys. 306(1), 43–54 (2016)
Nguyen, N.C., Fernandez, P., Freun, R., Peraire, J.: Accelerated residual methods for the iterative solution of systems of equations. SIAM J. Sci. Comput. 40(5), A3157–A3179 (2018)
Bohacek J, Kharicha A, Ludwig A, Wu M, Holzmann T, Karimi-Sibakib E. (2019) A GPU solver for symmetric positive-definite matrices vs. traditional codes, Comput Math Appl. 78(9):2933–2943
Lemita, S., Guebbai, H., Aissaoui, M.Z.: Generalized Jacobi method for linear bounded operators system. Comput. Appl. Math. 37(3), 3967–3980 (2018)
Yueh, WCh.: Eigenvalues of several tridiagonal matrices. Appl Math E-Notes 5, 66–74 (2005)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Kaveh, A., Rahami, H., Shojaei, I. (2020). Numerical Solution for System of Linear Equations Using Tridiagonal Matrix. In: Swift Analysis of Civil Engineering Structures Using Graph Theory Methods. Studies in Systems, Decision and Control, vol 290. Springer, Cham. https://doi.org/10.1007/978-3-030-45549-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-030-45549-1_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-45548-4
Online ISBN: 978-3-030-45549-1
eBook Packages: EngineeringEngineering (R0)