On the robustness of numerical algorithms for linear systems and signal processing in finite precision arithmetic

2015 ◽  
Vol 29 (12) ◽  
pp. 1539-1560
Author(s):  
Oumar Diene ◽  
Amit Bhaya
Keyword(s):  
Signal Processing ◽  
Linear Systems ◽  
Numerical Algorithms ◽  
Finite Precision ◽  
Finite Precision Arithmetic

scholarly journals Exploiting the Composite Step Strategy to the BiconjugateA-Orthogonal Residual Method for Non-Hermitian Linear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Yan-Fei Jing ◽  
Ting-Zhu Huang ◽  
Bruno Carpentieri ◽  
Yong Duan
Keyword(s):  
Convergence Rate ◽  
Linear Systems ◽  
Numerical Experiments ◽  
Numerical Instability ◽  
Finite Precision ◽  
Fast Convergence Rate ◽  
History Of ◽  
Finite Precision Arithmetic ◽  
A Minor ◽  
Biconjugate Gradient

The BiconjugateA-Orthogonal Residual (BiCOR) method carried out in finite precision arithmetic by means of the biconjugateA-orthonormalization procedure may possibly tend to suffer from two sources of numerical instability, known as two kinds of breakdowns, similarly to those of the Biconjugate Gradient (BCG) method. This paper naturally exploits the composite step strategy employed in the development of the composite step BCG (CSBCG) method into the BiCOR method to cure one of the breakdowns called as pivot breakdown. Analogously to the CSBCG method, the resulting interesting variant, with only a minor modification to the usual implementation of the BiCOR method, is able to avoid near pivot breakdowns and compute all the well-defined BiCOR iterates stably on the assumption that the underlying biconjugateA-orthonormalization procedure does not break down. Another benefit acquired is that it seems to be a viable algorithm providing some further practically desired smoothing of the convergence history of the norm of the residuals, which is justified by numerical experiments. In addition, the exhibited method inherits the promising advantages of the empirically observed stability and fast convergence rate of the BiCOR method over the BCG method so that it outperforms the CSBCG method to some extent.

scholarly journals Matrix Powers in Finite Precision Arithmetic

1995 ◽  
Vol 16 (2) ◽  
pp. 343-358 ◽  
Author(s):  
Nicholas J. Higham ◽  
Philip A. Knight
Keyword(s):  
Finite Precision ◽  
Finite Precision Arithmetic
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