Abstract
The CG-algorithm is an iterative method to solve linear systems
where A is a symmetric and positive definite coefficient matrix of order n. The method has been described first by Stiefel and Hesteness [1, 2] and additional information is contained in [3] and [4]. The notations used here coincide partially with those used in [5] where also the connexions with other methods and generalisations of the CG-algorithm are presented.
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References
Hestenes, M. R., Stiefel, E.: Methods of Conjugate Gradients for Solving Linear Systems. Nat. Bur. Standards J. of Res. 49, 409–436 (1952).
Stiefel, E.: Einige Methoden der Relaxationsrechnung. Z. Angew. Math. Phys. 3, 1–33 (1952).
Stiefel, E. Relaxationsmethoden bester Strategie zur Lösung linearer Gleichungssysteme. Comment. Math. Helv. 29, 157–179 (1955).
Stiefel, E. Kernel Polynomials in Linear Algebra and their Numerical Applications, Nat. Bur. Standards. Appl. Math. Ser. 49, 1–22 (1958).
Engeli, M., Ginsburg, Th., Rutishauser, H., Stiefel, E.: Refined Iterative Methods for Computation of the Solution and the Eigenvalues of Self-adjoint Boundary Value Problems. Mitt. Inst, angew. Math. ETH Zürich, No. 8 (Basel: Birkhäuser 1959).
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Ginsburg, T. (1971). The Conjugate Gradient Method. In: Bauer, F.L., Householder, A.S., Olver, F.W.J., Rutishauser, H., Samelson, K., Stiefel, E. (eds) Handbook for Automatic Computation. Die Grundlehren der mathematischen Wissenschaften, vol 186. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86940-2_5
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DOI: https://doi.org/10.1007/978-3-642-86940-2_5
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