A Generalised Conjugate Residual method for the solution of non-symmetric systems of equations with multiple right-hand sides

1999 ◽  
Vol 44 (5) ◽  
pp. 641-656 ◽  
Author(s):  
Frederik Jan Lingen
Keyword(s):  
Systems Of Equations ◽  
Residual Method ◽  
Right Hand ◽  
Conjugate Residual ◽  
Symmetric Systems

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

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1302
Author(s):  
Hong-Xiu Zhong ◽  
Xian-Ming Gu ◽  
Shao-Liang Zhang
Keyword(s):  
Linear Systems ◽  
Spectral Properties ◽  
Coefficient Matrix ◽  
Complex Symmetric Linear Systems ◽  
Right Hand ◽  
Orthogonality Conditions ◽  
Free Block ◽  
Complex Symmetric ◽  
The Right ◽  
Conjugate Residual

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.

The Conjugate Residual Method in Linesearch and Trust-Region Methods

2019 ◽  
Vol 29 (3) ◽  
pp. 1988-2025
Author(s):  
Marie-Ange Dahito ◽  
Dominique Orban
Keyword(s):  
Trust Region ◽  
Trust Region Methods ◽  
Residual Method ◽  
Conjugate Residual
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