Numerical Algorithms, ( ISI ), Volume (17), No (1), Year (1998-5) , Pages (105-119)

Title : ( The stable ATA-orthogonal s-step Orthomin(k) algorithm with the CADNA library )

Authors: Faezeh Toutounian Mashhad ,

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The major drawback of the s-step iterative methods for nonsymmetric linear systems of equations is that, in the floating-point arithmetic, a quick loss of orthogonality of s-dimensional direction subspaces can occur, and consequently slow convergence and instability in the algorithm may be observed as s gets larger than 5. In [18], Swanson and Chronopoulos have demonstrated that the value of s in the s-step Orthomin(k) algorithm can be increased beyond s = 5 by orthogonalizing the s direction vectors in each iteration, and have shown that the ATA-orthogonal s-step Orthomin(k) is stable for large values of s (up to s = 16). The subject of this paper is to show how by using the CADNA library, it is possible to determine a good value of s for ATA-orthogonal s-step Orthomin(k), and during the run of its code to detect the numerical instabilities and to stop the process correctly, and to restart the ATA-orthogonal s-step Orthomin(k) in order to improve the computed solution. Numerical examples are used to show the good numerical properties


, iterative methods, s-step methods, ATA-orthogonal s-step Orthomin(k), error propagation, CESTAC method, stochastic arithmetic, CADNA
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author = {Toutounian Mashhad, Faezeh},
title = {The stable ATA-orthogonal s-step Orthomin(k) algorithm with the CADNA library},
journal = {Numerical Algorithms},
year = {1998},
volume = {17},
number = {1},
month = {May},
issn = {1017-1398},
pages = {105--119},
numpages = {14},
keywords = {iterative methods; s-step methods; ATA-orthogonal s-step Orthomin(k); error propagation; CESTAC method; stochastic arithmetic; CADNA library},


%0 Journal Article
%T The stable ATA-orthogonal s-step Orthomin(k) algorithm with the CADNA library
%A Toutounian Mashhad, Faezeh
%J Numerical Algorithms
%@ 1017-1398
%D 1998