scholarly journals On the Solution of Skew-Symmetric Shifted Linear Systems

2006 ◽  
pp. 732-739
Author(s):  
T. Politi ◽  
A. Pugliese
Keyword(s):  
Linear Systems ◽  
Shifted Linear Systems

scholarly journals Nested Krylov Methods for Shifted Linear Systems

2015 ◽  
Vol 37 (5) ◽  
pp. S90-S112 ◽  
Author(s):  
Manuel Baumann ◽  
Martin B. van Gijzen
Keyword(s):  
Linear Systems ◽  
Krylov Methods ◽  
Shifted Linear Systems

Accelerated preconditioner updates for solving shifted linear systems

2016 ◽  
Vol 94 (4) ◽  
pp. 747-756
Author(s):  
Yu-Qin Bai ◽  
Ting-Zhu Huang ◽  
Wei-Hua Luo
Keyword(s):  
Linear Systems ◽  
Shifted Linear Systems

Solution of generalized shifted linear systems with complex symmetric matrices

2012 ◽  
Vol 231 (17) ◽  
pp. 5669-5684 ◽  
Author(s):  
Tomohiro Sogabe ◽  
Takeo Hoshi ◽  
Shao-Liang Zhang ◽  
Takeo Fujiwara
Keyword(s):  
Linear Systems ◽  
Symmetric Matrices ◽  
Shifted Linear Systems ◽  
Complex Symmetric ◽  
Complex Symmetric Matrices

scholarly journals BiCR-type methods for families of shifted linear systems

2014 ◽  
Vol 68 (7) ◽  
pp. 746-758 ◽  
Author(s):  
Xian-Ming Gu ◽  
Ting-Zhu Huang ◽  
Jing Meng ◽  
Tomohiro Sogabe ◽  
Hou-Biao Li ◽  
...  
Keyword(s):  
Linear Systems ◽  
Shifted Linear Systems

scholarly journals Nested Krylov methods for shifted linear systems

2015 ◽  
Author(s):  
Manuel Baumann ◽  
Martin B. van Gijzen
Keyword(s):  
Linear Systems ◽  
Invariance Property ◽  
Krylov Methods ◽  
Simultaneous Solution ◽  
Krylov Method ◽  
Shifted Linear Systems ◽  
Shift Invariance ◽  
Iterative Framework

Most algorithms for the simultaneous solution of shifted linear systems make use of the shift-invariance property of the underlying Krylov spaces. This particular comes into play when preconditioning is taken into account. We propose a new iterative framework for the solution of shifted systems that uses an inner multi-shift Krylov method as a preconditioner within a flexible outer Krylov method. Shift-invariance is preserved if the inner method yields collinear residuals.

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