Abstract
A class of iterative methods is presented for the solution of systems of linear equationsAx=b, whereA is a generalm ×n matrix. The methods are based on a development as a continued fraction of the inner product (r, r), wherer=b-Ax is the residual. The methods as defined are quite general and include some wellknown methods such as the minimal residual conjugate gradient method with one step.
Similar content being viewed by others
References
O. Axelsson,Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations, Linear Algebra and its Applications 29 (1980), 1–16.
M. R. Hestenes and E. Stiefel,Method of conjugate gradients for solving linear systems, J. Res. Bur. Standards, No. 49 (1952), 409–436.
F. Teixeira de Queiroz,The method of conjugate gradients presented as an open algorithm, Instituto Gulbenkian de Ciência, Portugal.
J. K. Reid,On the method of conjugate gradients for the solution of large sparse systems of linear equations. Proceedings of the conference on Large Sparse Sets of Linear Equations, ed. J. K. Reid, Academic Press (1971), 231–254.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Lindskog, G. The continued fraction methods for the solution of systems of linear equations. BIT 22, 519–527 (1982). https://doi.org/10.1007/BF01934414
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01934414