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- Title
A Breakdown-Free Block COCG Method for Complex Symmetric Linear Systems with Multiple Right-Hand Sides.
- Authors
Zhong, Hong-Xiu; Gu, Xian-Ming; Zhang, Shao-Liang
- Abstract
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.
- Subjects
CONJUGATE gradient methods; SYMMETRIC matrices
- Publication
Symmetry (20738994), 2019, Vol 11, Issue 10, p1302
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym11101302