Geodesic
Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother
Applications of Mathematics, Tome 62 (2017) no. 1, pp. 49-73.

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We extend the analysis of the recently proposed nonlinear EIS scheme applied to the partial eigenvalue problem. We address the case where the Rayleigh quotient iteration is used as the smoother on the fine-level. Unlike in our previous theoretical results, where the smoother given by the linear inverse power method is assumed, we prove nonlinear speed-up when the approximation becomes close to the exact solution. The speed-up is cubic. Unlike existent convergence estimates for the Rayleigh quotient iteration, our estimates take advantage of the powerful effect of the coarse-space.
DOI : 10.21136/AM.2017.0101-16
Classification : 65F15, 65N55
Keywords: nonlinear multigrid; exact interpolation scheme 
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     title = {Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and {Rayleigh} quotient iteration nonlinear smoother},
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Vaněk, Petr; Pultarová, Ivana. Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother. Applications of Mathematics, Tome 62 (2017) no. 1, pp. 49-73. doi : 10.21136/AM.2017.0101-16. http://geodesic.mathdoc.fr/articles/10.21136/AM.2017.0101-16/

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