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A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides

1
School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China
2
School of Economic Mathematics/Institute of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, Sichuan, China
3
Department of Applied Physics, Graduate School of Engineering, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(10), 1302; https://doi.org/10.3390/sym11101302
Received: 19 September 2019 / Revised: 12 October 2019 / Accepted: 14 October 2019 / Published: 16 October 2019
The block conjugate orthogonal conjugate gradient method (BCOCG) is recognized as a common method to solve complex symmetric linear systems with multiple right-hand sides. However, breakdown always occurs if the right-hand sides are rank deficient. In this paper, based on the orthogonality conditions, we present a breakdown-free BCOCG algorithm with new parameter matrices to handle rank deficiency. To improve the spectral properties of coefficient matrix A, a precondition version of the breakdown-free BCOCG is proposed in detail. We also give the relative algorithms for the block conjugate A-orthogonal conjugate residual method. Numerical results illustrate that when breakdown occurs, the breakdown-free algorithms yield faster convergence than the non-breakdown-free algorithms. View Full-Text
Keywords: COCG; COCR; breakdown-free; complex symmetric matrix; rank deficiency; multiple right-hand sides COCG; COCR; breakdown-free; complex symmetric matrix; rank deficiency; multiple right-hand sides
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Zhong, H.-X.; Gu, X.-M.; Zhang, S.-L. A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides. Symmetry 2019, 11, 1302.

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