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International Journal of Computer Mathematics Volume 82, 2005 - Issue 7
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Original Articles

Restarted GMRES augmented with harmonic Ritz vectors for shifted linear systems

Guiding Gu Department of Applied Mathematics, Shanghai University of Finance and Economics, Shanghai, 200433, P.R. ChinaCorrespondence[email protected]
Pages 837-849 | Received 17 Aug 2004, Published online: 25 Jan 2007

Citations (11)

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Qiang Niu, Linzhang Lu & Jituan Zhou. (2010) Accelerate weighted GMRES by augmenting error approximations. International Journal of Computer Mathematics 87:9, pages 2101-2112.
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Articles from other publishers (10)

Lakhdar Elbouyahyaoui, Mohammed Heyouni, Azita Tajaddini & Farid Saberi-Movahed. (2020) On restarted and deflated block FOM and GMRES methods for sequences of shifted linear systems. Numerical Algorithms 87:3, pages 1257-1299.
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Xian-Ming Gu, Ting-Zhu Huang, Bruno Carpentieri, Akira Imakura, Ke Zhang & Lei Du. (2020) Efficient variants of the CMRH method for solving a sequence of multi-shifted non-Hermitian linear systems simultaneously. Journal of Computational and Applied Mathematics 375, pages 112788.
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Rui-Rui Wang, Qiang Niu, Xiao-Bin Tang & Xiang Wang. (2019) Solving shifted linear systems with restarted GMRES augmented with error approximations. Computers & Mathematics with Applications 78:6, pages 1910-1918.
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Hong-Xiu Zhong & Xian-Ming Gu. (2019) A flexible and adaptive Simpler GMRES with deflated restarting for shifted linear systems. Computers & Mathematics with Applications 78:3, pages 997-1007.
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Z. Ramezani & F. Toutounian. (2018) Extended and rational Hessenberg methods for the evaluation of matrix functions. BIT Numerical Mathematics 59:2, pages 523-545.
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Xian-Ming Gu, Ting-Zhu Huang, Guojian Yin, Bruno Carpentieri, Chun Wen & Lei Du. (2018) Restarted Hessenberg method for solving shifted nonsymmetric linear systems. Journal of Computational and Applied Mathematics 331, pages 166-177.
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Mehdi Dehghan & Reza Mohammadi-Arani. (2016) Generalized product-type methods based on bi-conjugate gradient (GPBiCG) for solving shifted linear systems. Computational and Applied Mathematics 36:4, pages 1591-1606.
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Lei Du, Tomohiro Sogabe & Shao-Liang Zhang. (2015) IDR( ) for solving shifted nonsymmetric linear systems . Journal of Computational and Applied Mathematics 274, pages 35-43.
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Igor Moret & Marina Popolizio. (2014) The restarted shift-and-invert Krylov method for matrix functions. Numerical Linear Algebra with Applications 21:1, pages 68-80.
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Yan-Fei Jing & Ting-Zhu Huang. (2009) Restarted weighted full orthogonalization method for shifted linear systems. Computers & Mathematics with Applications 57:9, pages 1583-1591.
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