Abstract
Abstract — We treat systematically the preconditioned steepest ascent method and the preconditioned conjugate gradient method for eigenvalue problems and present convergence rate estimates. We also suggest a modification of the methods, that makes it possible to implement them in a subspace (such as that of mesh functions, defined in the mesh-points on the dividing line for the domain decomposition methods). We discuss as an example an eigenvalue problem for -Δ h (a mesh discretisation of Laplacian) and show that the rate of convergence does not slow as h → 0.
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Knyazev, A.V. (1991). A Preconditioned Conjugate Gradient Method for Eigenvalue Problems and its Implementation in a Subspace. In: Albrecht, J., Collatz, L., Hagedorn, P., Velte, W. (eds) Numerical Treatment of Eigenvalue Problems Vol. 5 / Numerische Behandlung von Eigenwertaufgaben Band 5. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 96. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6332-2_11
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DOI: https://doi.org/10.1007/978-3-0348-6332-2_11
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