na5
swMATH ID:  11489 
Software Authors:  Brezinski, C.; RedivoZaglia, M. 
Description:  Treatment of nearbreakdown in the CGS algorithm. Lanczos’ method for solving the system of linear equationsAx=b consists in constructing a sequence of vectors (x k ) such thatr k =b−Ax k =P k (A)r 0 wherer 0=b−Ax 0.P k is an orthogonal polynomial which is computed recursively. The conjugate gradient squared algorithm (CGS) consists in takingr k =P k 2 (A)r0. In the recurrence relation forP k , the coefficients are given as ratios of scalar products. When a scalar product in a denominator is zero, then a breakdown occurs in the algorithm. When such a scalar product is close to zero, then rounding errors can seriously affect the algorithm, a situation known as nearbreakdown. In this paper it is shown how to avoid nearbreakdown in the CGS algorithm in order to obtain a more stable method. 
Homepage:  http://www.netlib.org/numeralgo/index.html 
Keywords:  orthogonal polynomials; numerical examples; nearbreakdown situation; conjugate gradient squared algorithm; CGS algorithm; Lanczos’ method; recurrence relations; method of recursive zoom algorithm 
Related Software:  na1; CGS; BiCGstab; GpBiCg; ARPACK; JDQR; DSUBSP; LSQR; MA32; MA42; MA47; DRIC; ScaLAPACK; LAPACK; testmatrix; QMRPACK; JDQZ; eigs; SRRIT; RODAS 
Cited in:  24 Publications 
Standard Articles
1 Publication describing the Software, including 1 Publication in zbMATH  Year 

Treatment of nearbreakdown in the CGS algorithm. Zbl 0810.65028 Brezinski, C.; RedivoZaglia, M. 
1994

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Cited by 20 Authors
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Cited in 11 Serials
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