{"title":"A New Seed Projection Method for Solving Shifted Systems with Multiple Right-Hand Sides","authors":"Chao Li,Hao Liu","volume":76,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":639,"pagesEnd":642,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/16784","abstract":"<p>In this paper, we propose a new seed projection method for solving shifted systems with multiple right-hand sides. This seed projection method uses a seed selection strategy. Numerical experiments are presented to show the efficiency of the newly method.<\/p>\r\n","references":"<p>[1] A. Feriani, F. Perotti, V. Simoncini, Iterative system solvers for the\r\nfrequency analysis of linear mechanical systems, Comput. Methods Appl.\r\nMech. and Engrg. 190 (13-14) (2000) 1719-1739.\r\n[2] V. Simoncini, Restarted full orthogonalization method for shifted linear\r\nsystems, BIT (Numer. Math.) 43 (2003) 459-466.\r\n[3] D. O\u2019Leary, The block conjugate gradient algorithm and related methods,\r\nLinear Algebra Appl. 29 (1980) 293-322.\r\n[4] C. Smith, A. Peterson and R. Mittra, A conjugate gradient algorithm\r\nfor treatment of multiple incident electromagnetic fields, IEEE Trans.\r\nAntennas Propagation 37 (1989) 1490-1493.\r\n[5] R.W.Freund, Solution of shifted linear systems by quasi-minimal residual\r\niterations, Numerical Linear Algebra (1993) 101-121.\r\n[6] A.Frommer and U.Glassner, Restarted GMRES for shifted linear systems,\r\nSIAM J. Sci. Comput. 19 (1998) 15-26.\r\n[7] GuiDing Gu, Wenyue Zhu, Seed projection methods for solving unsymmetric\r\nshifted systems with multiple right-hand sides, Mathematica\r\nNumerica Sinica 26 (2004) 211-224(In Chinese).\r\n[8] GuiDing Gu, A seed method for solving nonsymmetric linear systems\r\nwith multiple right-hand sides, Intern. J. Computer Math. 79 (2002) 307-\r\n326.\r\n[9] V. Simoncini, E. Gallopolous, An iterative method for nonsymmetric\r\nsystems with multiple right-hand sides, SIAM J. Sci. Comput.16 (1995)\r\n917-933.<\/p>\r\n","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 76, 2013"}

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