An error bound for the MAOR method. (English) Zbl 1053.65019
The modified accelerated overrelaxation (MAOR) method for the iterative solution of \(Ax=b\) with \(A\) symmetric positive definite and consistently ordered depends on three parameters \(\omega_1,\omega_2,\gamma\). In this paper, a bound is given for \(\epsilon_k=x-x^k\) in terms of these three parameters, and on \(\| \delta_k\| \), \(\| \delta_{k+1}\| \), and \(\delta_k^T\delta_{k+1}\) where \(\delta_j = x^j-x^{j-1}\), \(j=k,k+1\). As special cases, classical results are found for the AOR method studied by Y. Z. Song [BIT 39, No. 2, 373–383 (1999; Zbl 0961.65030)] and the SOR by T. R. Hatcher [SIAM J. Numer. Anal. 19, 930–941 (1982; Zbl 0499.65020)].
Reviewer: Adhemar Bultheel (Leuven)
MSC:
| 65F10 | Iterative numerical methods for linear systems |
References:
| [1] | Hadjidimos, A.; Psimarni, A.; Yeyios, A. K., On the convergence of the modified accelerated overrelaxation (MAOR) method, Appl. Num. Math., 10, 115-127 (1992) · Zbl 0754.65035 |
| [2] | Young, D. M., Iterative Solution of Large Linear Systems (1971), Academic Press: Academic Press New York · Zbl 0204.48102 |
| [3] | Song, Y. Z., On the convergence of the MAOR method, J. Comp. Appl. Math., 79, 299-317 (1997) · Zbl 0882.65017 |
| [4] | Hatcher, T. R., An error bound for certain successive overrelaxation schemes, SIAM J. Num. Anal., 19, 930-941 (1982) · Zbl 0499.65020 |
| [5] | Song, Y. Z., A note on an error bound for the AOR method, BIT, 39, 2, 373-383 (1999) · Zbl 0961.65030 |
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