Abstract
We start with recalling one of the many definitions of the conjugate gradient method for the approximation of the solution x of a linear system Ax=b with symmetric and positive definite system matrix A. An advantage of this definition is that it is easy to state, and that it immediately shows the connection with the Lanczos method for approximation of eigenvalues of A. A disadvantage is that the actual algorithms for both the conjugate gradients and the Lanczos method do not follow too easily and require clever combination of several ingredients.
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Brandts, J., van der Vorst, H. (2004). The Convergence of Krylov Methods and Ritz Values. In: KřÞek, M., Neittaanmäki, P., Korotov, S., Glowinski, R. (eds) Conjugate Gradient Algorithms and Finite Element Methods. Scientific Computation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18560-1_4
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DOI: https://doi.org/10.1007/978-3-642-18560-1_4
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