BIT Numerical Mathematics

, Volume 22, Issue 4, pp 519–527 | Cite as

The continued fraction methods for the solution of systems of linear equations

  • Gunhild Lindskog
Part II Numerical Mathematics

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.

Keywords

Linear Equation Computational Mathematic Iterative Method Conjugate Gradient Gradient Method 

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References

  1. 1.
    O. Axelsson,Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations, Linear Algebra and its Applications 29 (1980), 1–16.Google Scholar
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    M. R. Hestenes and E. Stiefel,Method of conjugate gradients for solving linear systems, J. Res. Bur. Standards, No. 49 (1952), 409–436.Google Scholar
  3. 3.
    F. Teixeira de Queiroz,The method of conjugate gradients presented as an open algorithm, Instituto Gulbenkian de Ciência, Portugal.Google Scholar
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    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.Google Scholar

Copyright information

© BIT Foundations 1982

Authors and Affiliations

  • Gunhild Lindskog
    • 1
  1. 1.Department of Computer SciencesChalmers University of Technology and the University of GöteborgGöteborgSweden

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