Article Contents
Article Contents

A generalized projection iterative method for solving non-singular linear systems

• *Corresponding author: Manideepa Saha

The work was supported by Department of Science and Technology-Science and Engineering Research Board (grant no. ECR/2017/002116)

• In this paper, we propose and analyze iterative method based on projection techniques to solve a non-singular linear system $Ax = b$. In particular, for a given positive integer $m$, $m$-dimensional successive projection method ($m$D-SPM) for symmetric positive definite matrix $A$, is generalized for non-singular matrix $A$. Moreover, it is proved that $m$D-SPM gives better result for large values of $m$. Numerical experiments are carried out to demonstrate the superiority of the proposed method in comparison with other schemes in the scientific literature.

Mathematics Subject Classification: Primary: 15A06, 65F10.

 Citation:

• Table 1.  Results for 4.1

 Iteration Process No of Iterations Relative Residual GMRES 9 $1.2 \times 10^{-7}$ LSQR 7 $5.5 \times 10^{-8}$ $3$D-OPM 20 $6.7857 \times 10^{-7}$ $10$D-OPM 6 $5.9894\times 10^{-7}$ $20$D-OPM 3 $5.0539\times 10^{-7}$ $50$D-OPM 2 $2.0235\times 10^{-11}$

Table 2.  Results for 4.2

 Iteration Process No of Iterations Relative Residual GMRES 9 $1.9 \times 10^{-7}$ BiCG 9 $2.0 \times 10^{-7}$ LSQR 2 $3.2 \times 10^{-16}$ $3$D-OPM 3 $4.5922 \times 10^{-7}$ $10$D-OPM 1 $9.5332\times 10^{-8}$ $20$D-OPM 1 $9.1\times 10^{-15}$ $50$D-OPM 1 $6.3231\times 10^{-17}$

Table 3.  Results for 4.3

 Iteration Process No of Iterations Relative Residual GMRES 10 $2.7 \times 10^{-7}$ BiCG 10 $2.8 \times 10^{-7}$ LSQR 13 $7.4 \times 10^{-7}$ $3$D-OPM 4 $4.6042 \times 10^{-7}$ $10$D-OPM 2 $2.62\times 10^{-11}$ $20$D-OPM 1 $1.9751\times 10^{-11}$
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