پیوندهای مفید
آمار
| تعداد نشریات | 26 |
| تعداد شماره‌ها | 308 |
| تعداد مقالات | 2,680 |
| تعداد مشاهده مقاله | 4,015,868 |
| تعداد دریافت فایل اصل مقاله | 2,706,644 |
A fourth-order iterative method for computing the moore-penrose inverse | ||
| Journal of Hyperstructures | ||
| دوره 6، شماره 1، شهریور 2017، صفحه 52-67 اصل مقاله (326.47 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2017.2661 | ||
| نویسندگان | ||
| H. Esmaeili* ؛ R. Erfanifar؛ M. Rashidi | ||
| Department of Mathematics, Bu-Ali Sina University, Hamedan, Iran | ||
| چکیده | ||
| In this study, a new fourth-order method to compute the Moore-Penrose inverse is proposed. Convergence analysis along with the error estimates of the method is investigated. Every iteration of the method involves four matrix multiplications. A wide set of numerical comparisons of the proposed method with nine higher order methods shows that the average number of matrix multiplications and the average CPU time of our method are considerably less than those of other methods. | ||
| کلیدواژه‌ها | ||
| Moore-Penrose inverse؛ Iterative method؛ Schulz-type method؛ Fourth-order convergence؛ Matrix multiplication | ||
| مراجع | ||
|
[1] A. Ben-Israel, D. Cohen, On iterative computation of generalized inverses and associated projections, SlAM J. Numer. Anal. 3 (1966), 410–419. [2] A. Ben-Israel, T.N.E. Greville, Generalized Inverses, Second ed., New York:Springer (2003). [3] R.L. Burden, J.D. Faires, Numerical Analysis, 9th Ed. Brooks/Cole, Cengage Learning, Boston (2011). [4] H. Chen, Y. Wang, A family of higher-order convergent iterative methods for computing the Moore-Penrose inverse, Appl. Math. Comput. 218 (2011), 4012–4016. [5] A. Cichocki, B. Unbehauen, Neural networks for optimization and signal pro-cessing, New York: John Wiley & Sons (1993). [6] E.V. Krishnamurthy, S.K. Sen, Numerical Algorithms: Computations in Science and Engineering, New Delhi, India: Affiliated East-West Press (1986). [7] W. Li, Z. Li, A family of iterative methods for computing the approximate in-verse of a square matrix and inner inverse of a non-square matrix, Appl. Math.Comput. 215 (2010), 3433–3442. [8] H. B. Li, T.Z. Huang, Y. Zhang, X.P. Liu, T.X. Gu, Chebyshev-type methods and preconditioning techniques, Appl. Math. Comput. 218 (2001), 260–270. [9] S. Miljkovi´c, M. Miladinovi´c, P., Stanimirovi´c, I. Stojanovi´c, Application of the pseudo-inverse computation in reconstruction of blurred images, Filomat 26 (2012), 453–465. [10] H.S. Najafi, M.S. Solary, Computational algorithms for computing the inverse of a square matrix, quasi-inverse of a non-square matrix and block matrices, Appl. Math. Comput. 183 (2006), 539–550. [11] V.Y. Pan, R. Schreiber, An improved Newton iteration for the generalized inverse of a matrix with applications, SIAM J. Sci. Stat. Comput. 12 (1991), 1109–1131. [12] V.Y. Pan, Newton’s iteration for matrix inversion, advances and extensions, ma-trix methods: theory algorithms and applications, Singapore: World Scientific (2010). [13] W.H. Pierce, A self-correcting matrix iteration for the Moore-Penrose inverse,Linear Algebra Appl. 244 (1996), 357-363. [14] P. Roland, P.G. Beim, Inverse problems in neural field theory, SIAM J. Appl. Dynam. Sys. 8 (2009), 1405–1433. [15] G. Schulz, Iterative Berechmmg der reziproken Matrix, Z. Angew. Math. Mech.13 (1933), 57–59. [16] L. Sciavicco, B. Siciliano, Modelling and control of robot manipulators, London:Springer–Verlag (2000). [17] X. Sheng, G. Chen: The generalized weighted Moore-Penrose inverse, J. Appl.Math. Comput. 25 (2007), 407–413. [18] F. Soleymani, P.S. Stanimirovi´c, A Higher Order Iterative Method for Computing the Drazin Inverse, The Scientific World Journal Volume 2013, Article ID 708647,11 pages, http://dx.doi.org/10.1155/2013/708647. [19] F. Soleymani, P.S. Stanimirovi´c, M.Z. Ullah, An accelerated iterative method for computing weighted Moore-Penrose inverse, Appl. Math. Comput. 222 (2013),365–371. [20] F. Soleymani, H. Salmani, M. Rasouli, Finding the Moore-Penrose inverse by a new matrix iteration, J. Appl. Math. Comput. 47 (2015), 33-48. [21] S. Srivastava, D.K. Gupta, A higher order iterative method for A(2)T ,S, J. Appl.Math. Comput. 46 (2014), 147–168. [22] P.S. Stanimirovi´c, D.S. Cvetkovi´c-Ili´c, Successive matrix squaring algorithm for computing outer inverses, Appl. Math. Comput. 203 (2008), 19–29. [23] F. Toutounian, F. Soleymani, An iterative method for computing the approximate inverse of a square matrix and the Moore-Penrose inverse of a non-square matrix, Appl. Math. Comput. 224 (2013), 671–680. [24] L. Weiguo, L. Juan, Q. Tiantian, A family of iterative methods for computing Moore-Penrose inverse of a matrix, Linear Algebra Appl. 438 (2013), 47-56. | ||
|
آمار تعداد مشاهده مقاله: 13 تعداد دریافت فایل اصل مقاله: 32 |
||