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 JAMP  Vol.6 No.2 , February 2018
Efficient Iterative Method for Solving the General Restricted Linear Equation
Abstract: An iterative method is developed for solving the solution of the general restricted linear equation. The convergence, stability, and error estimate are given. Numerical experiments are presented to demonstrate the efficiency and accuracy.
Cite this paper: Liu, X. , Du, W. , Yu, Y. and Qin, Y. (2018) Efficient Iterative Method for Solving the General Restricted Linear Equation. Journal of Applied Mathematics and Physics, 6, 418-428. doi: 10.4236/jamp.2018.62039.
References

[1]   Ben-Israel, A. and Greville, T.N.E. (2003) Generalized Inverses. Volume 15 of CMS Books in Mathematics/Ouvrages de Mathématiques de la SMC, 2nd Edition, Springer-Verlag, New York.

[2]   Chen, Y.L. (1993) A Cramer Rule for Solution of the General Restricted Linear Equation. Linear and Multilinear Algebra, 34, 177-186.
https://doi.org/10.1080/03081089308818219

[3]   Wei, Y.M. and Wu, H.B. (2001) Splitting Methods for Computing the Generalized Inverse and Rectangular Systems. International Journal of Computer Mathematics, 77, 401-424.
https://doi.org/10.1080/00207160108805075

[4]   Srivastava, S. and Gupta, D.K. (2015) An Iterative Method for Solving General Restricted Linear Equations. Applied Mathematics and Computation, 262, 344-353.
https://doi.org/10.1016/j.amc.2015.04.047

[5]   Song, G.J., Wang, Q.-W. and Chang, H.-X. (2011) Cramer Rule for the Unique Solution of Restricted Matrix Equations over the Quaternion Skew field. Computers & Mathematics with Applications, 61, 1576-1589.
https://doi.org/10.1016/j.camwa.2011.01.026

[6]   Chen, Y.L. (1997) Iterative Methods for Solving Restricted Linear Equations. Applied Mathematics and Computation, 86, 171-184.
https://doi.org/10.1016/S0096-3003(96)00180-4

[7]   Wei, Y.M., Li, X.Z. and Wu, H.B. (2003) Subproper and Regular Splittings for Restricted Rectangular Linear System. Applied Mathematics and Computation, 136, 535-547.
https://doi.org/10.1016/S0096-3003(02)00078-4

[8]   Yu, Y.M. (2008) PCR Algorithm for Parallel Computing the Solution of the General Restricted Linear Equations. Journal of Applied Mathematics and Computing, 27, 125-136.
https://doi.org/10.1007/s12190-008-0062-3

[9]   Song, G.-J. and Dong, C.-Z. (2017) New Results on Condensed Cramer’s Rule for the General Solution to Some Restricted Quaternion Matrix Equations. Journal of Applied Mathematics and Computing, 53, 321-341.
https://doi.org/10.1007/s12190-015-0970-y

[10]   Cai, J. and Chen, G.L. (2007) On Determinantal Representation for the Generalized Inverse and Its Applications. Numerical Linear Algebra with Applications, 14, 169-182.
https://doi.org/10.1002/nla.513

[11]   Liu, X.J., Zhu, G.Y., Zhou, G.P. and Yu, Y.M. (2012) An Analog of the Adjugate Matrix for the Outer Inverse . Mathematical Problems in Engineering, Article ID: 591256.

[12]   Roger, A.H. and Johnson, C.R. (2013) Matrix Analysis. 2nd Edition, Cambridge University Press, Cambridge.

[13]   Liu, X.J., Jin, H.W. and Yu, Y.M. (2013) Higher-Order Convergent Iterative Method for Computing the Generalized Inverse and Its Application to Toeplitz Matrices. Linear Algebra and Its Applications, 439, 1635-1650.
https://doi.org/10.1016/j.laa.2013.05.005

[14]   Srivastava, S., Stanimirovic, P.S., Katsikis, V.N. and Gupta, D.K. (2017) A Family of Iterative Methods with Accelerated Convergence for Restricted Linear System of Equations. Mediterranean Journal of Mathematics, 14, 222.
https://doi.org/10.1007/s00009-017-1020-9

 
 
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