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Advances in Mathematical Physics
Volume 2015, Article ID 103074, 7 pages
Research Article

A Simpler GMRES Method for Oscillatory Integrals with Irregular Oscillations

1Department of Mathematics and Computational Science, Hunan University of Science and Engineering, Yongzhou 425100, China
2International College, Central South University of Forestry and Technology, Changsha 410083, China

Received 2 April 2015; Accepted 4 June 2015

Academic Editor: Ming Mei

Copyright © 2015 Qinghua Wu and Meiying Xiang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A simpler GMRES method for computing oscillatory integral is presented. Theoretical analysis shows that this method is mathematically equivalent to the GMRES method proposed by Olver (2009). Moreover, the simpler GMRES does not require upper Hessenberg matrix factorization, which leads to much simpler program and requires less work. Numerical experiments are conducted to illustrate the performance of the new method and show that in some cases the simpler GMRES method could achieve higher accuracy than GMRES.