پیوندهای مفید
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 391 |
| تعداد مقالات | 3,425 |
| تعداد مشاهده مقاله | 5,264,868 |
| تعداد دریافت فایل اصل مقاله | 3,600,313 |
An efficient iterative method for solving large linear systems | ||
| Journal of Hyperstructures | ||
| دوره 9، شماره 1، شهریور 2020، صفحه 62-74 اصل مقاله (343.71 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2020.2627 | ||
| نویسندگان | ||
| Ali Jamalian* 1؛ Hossein Aminikhah2 | ||
| 1Department of Computer Science, University of Guilan, P.O.Box 41335-19141, Rasht,Iran | ||
| 2Department of Applied Mathematics and Department of Computer Science, University of Guilan, P.O.Box 41335-19141, Rasht, Iran Center of Excellence for Mathematical Modelling, Optimization and Combinational Computing (MMOCC), University of Guilan, P.O.Box 41938-19141, Rasht, Iran. | ||
| چکیده | ||
| This paper presents a new powerful iterative method for solving large and sparse linear systems. Using the idea of the Jaya method to the restarted generalized minimum residual (GMRES) method, we propose the Jaya-GMRES method. The JayaGMRES is an efficient solver, being based mainly on matrix-vector multiplications. Numerical results show that the Jaya-GMRES method has found more accurate solutions and converges much regular than the GMRES method. | ||
| کلیدواژه‌ها | ||
| GMRES method؛ Jaya optimization algorithm؛ Linear systems؛ Iterative method؛ Non-symmetric matrix | ||
| مراجع | ||
|
[1] W. E. Arnoldi, The principle of minimized interations in the solution of the matrix eigenvalue problem, Quarterly of applied mathematics, 9 (1) (1951) 17-29. [2] P. G. Ciarlet, Introduction to Numerical Linear Algebra and Optimisation, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, (1989). [3] I. S. Du , R. G. Grimes and J. G. Lewis, User's guide for the Harwell{Boeing sparse matrix collection (Release I), Technical Report TR/PA/92/86, CERFACS, Toulouse, France (1992). [4] W. Ford, Numerical Linear Algebra with Applications, Academic Press, USA, (2015). [5] L. Hogben, Handbook of linear algebra, Chapman & Hall/CRC, New York, USA, (2007). [6] R. B. Morgan, A restarted GMRES method augmented with eigenvectors, SIAM Journal on Matrix Analysis and Applications, 16 (4) (1995) 1154-1171. [7] R. Rao, Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems, International Journal of Industrial Engineering Computations, 7 (1) (2016) 19-34. [8] R. V. Rao, Jaya: an advanced optimization algorithm and its engineering applications, Cham: SpringerInternational Publishing, (2019). [9] Y. Saad, Variations on Arnoldi's method for computing eigenelements of large unsymmetric matrices, Linear algebra and its applications, 34 (1980) 269-295. [10] Y. Saad, Krylov subspace methods for solving large unsymmetric linear systems, Mathematics of computation, 37 (155) (1981) 105-126. [11] Y. Saad, Iteractive Method for Sparse Linear Systems, PWS Publishing Company, a division of International Thomson Publishing Inc., USA, (1996). [12] Y. Saad, Schultz, Martin, H. GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems, SIAM Journal on scientific and statistical computing, 7 (1986) 856-869. [13] L. N. Trefethen and D. Bau, Numerical Linear Algebra, SIAM, (1997). [14] D. S.Watkins, Fundamentals of Matrix Computations, third ed.,Wiley, Hoboken, NJ, (2010). [15] H. Wendland, Numerical Linear Algebra, Cambridge Texts in Applied Mathematics. Cambridge University Press, (2018). | ||
|
آمار تعداد مشاهده مقاله: 61 تعداد دریافت فایل اصل مقاله: 129 |
||