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

• Main Authors: Hong-Xiu Zhong, Xian-Ming Gu, Shao-Liang Zhang
• Format: Article
• Language: English
• Published: MDPI AG 2019-10-01
• Series: Symmetry
• Subjects: cocg; cocr; breakdown-free; complex symmetric matrix; rank deficiency; multiple right-hand sides
• Online Access: https://www.mdpi.com/2073-8994/11/10/1302

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 <i>A</i>, a precondition version of the breakdown-free BCOCG is proposed in detail. We also give the relative algorithms for the block conjugate <i>A</i>-orthogonal conjugate residual method. Numerical results illustrate that when breakdown occurs, the breakdown-free algorithms yield faster convergence than the non-breakdown-free algorithms.