Applications of Mathematics

, Volume 62, Issue 1, pp 49–73 | Cite as

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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Abstract

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.

Keywords

nonlinear multigrid exact interpolation scheme 

MSC 2010

65N55 

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of West BohemiaPlzeňCzech Republic
  2. 2.Department of Mathematics, Faculty of Civil EngineeringCzech Technical University in PraguePraha 6Czech Republic
  3. 3.Department of MathematicsCollege of Polytechnics JihlavaJihlavaCzech Republic

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