Abstract
Recently, Axelsson and Salkuyeh in (BIT Numerical Mathematics, 59 (2019) 321–342) proposed the transformed matrix iteration (TMIT) method for solving a certain two-by-two block matrices with square blocks. However, they did not present any formula for the optimal parameter of the method which minimizes the spectral radius of the iteration matrix. In this work, we give an upper bound for the spectral radius of the iteration matrix of the method and then compute the parameter which minimizes this upper bound. Numerical results are presented to demonstrate the theoretical results.
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Acknowledgments
The authors would like to thank the referees for their careful reading of the paper and giving several helpful comments. The work of Davod Khojasteh Salkuyeh is partially supported by University of Guilan.
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Siahkolaei, T.S., Salkuyeh, D.K. On the parameter selection in the transformed matrix iteration method. Numer Algor 86, 179–189 (2021). https://doi.org/10.1007/s11075-020-00884-y
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DOI: https://doi.org/10.1007/s11075-020-00884-y