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Volume 1, Issue 1
A Global Property of Restarted FOM Algorithm

J. Info. Comput. Sci. , 1 (2006), pp. 11-20.

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  • Abstract
In this paper an interesting property of the restarted FOM algorithm for solving large nonsymmetric linear systems is presented and studied. By establishing a relationship between the convergence of its residual vectors and the convergence of Ritz values in the Arnoldi procedure, it is shown that some important information of previous FOM(m) cycles may be saved by the iteration approximates at the time of restarting, with which the FOM(m) cycles can complement one another harmoniously in reducing the iteration residual. Based on the study of FOM(m), two polynomial preconditioning techniques are proposed; one is for solving nonsymmetric linear systems and another is for forming an effective starting vector in the restarted Arnoldi method for solving nonsymmetric eigenvalue problems.
  • Keywords

nonsymmetric linear systems, nonsymmetric eigenvalue problems, iterative methods, FOM, Arnoldi’s method, restarting polynomial preconditioning.

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COPYRIGHT: © Global Science Press

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@Article{JICS-1-11, author = {}, title = {A Global Property of Restarted FOM Algorithm}, journal = {Journal of Information and Computing Science}, year = {2024}, volume = {1}, number = {1}, pages = {11--20}, abstract = { In this paper an interesting property of the restarted FOM algorithm for solving large nonsymmetric linear systems is presented and studied. By establishing a relationship between the convergence of its residual vectors and the convergence of Ritz values in the Arnoldi procedure, it is shown that some important information of previous FOM(m) cycles may be saved by the iteration approximates at the time of restarting, with which the FOM(m) cycles can complement one another harmoniously in reducing the iteration residual. Based on the study of FOM(m), two polynomial preconditioning techniques are proposed; one is for solving nonsymmetric linear systems and another is for forming an effective starting vector in the restarted Arnoldi method for solving nonsymmetric eigenvalue problems. }, issn = {1746-7659}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22855.html} }
TY - JOUR T1 - A Global Property of Restarted FOM Algorithm AU - JO - Journal of Information and Computing Science VL - 1 SP - 11 EP - 20 PY - 2024 DA - 2024/01 SN - 1 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jics/22855.html KW - nonsymmetric linear systems, nonsymmetric eigenvalue problems, iterative methods, FOM, Arnoldi’s method, restarting KW - polynomial preconditioning. AB - In this paper an interesting property of the restarted FOM algorithm for solving large nonsymmetric linear systems is presented and studied. By establishing a relationship between the convergence of its residual vectors and the convergence of Ritz values in the Arnoldi procedure, it is shown that some important information of previous FOM(m) cycles may be saved by the iteration approximates at the time of restarting, with which the FOM(m) cycles can complement one another harmoniously in reducing the iteration residual. Based on the study of FOM(m), two polynomial preconditioning techniques are proposed; one is for solving nonsymmetric linear systems and another is for forming an effective starting vector in the restarted Arnoldi method for solving nonsymmetric eigenvalue problems.
. (2024). A Global Property of Restarted FOM Algorithm. Journal of Information and Computing Science. 1 (1). 11-20. doi:
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