Geodesic
An imperfect conjugate gradient algorithm
Applications of Mathematics, Tome 27 (1982) no. 6, pp. 426-432.

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A new biorthogonalization algorithm is defined which does not depend on the step-size used. The algorithm is suggested so as to minimize the total error after $n$ steps if imperfect steps are used. The majority of conjugate gradient algorithms are sensitive to the exactness of the line searches and this phenomenon may destroy the global efficiency of these algorithms.
DOI : 10.21136/AM.1982.103989
Classification : 65F10, 65K05, 90C25
Keywords: imperfect conjugate gradient algorithm; symmetric, positive definite matrix; biorthogonalization; line searches; global efficiency 
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Sloboda, Fridrich. An imperfect conjugate gradient algorithm. Applications of Mathematics, Tome 27 (1982) no. 6, pp. 426-432. doi : 10.21136/AM.1982.103989. http://geodesic.mathdoc.fr/articles/10.21136/AM.1982.103989/

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