Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother

Vaněk, Petr, and 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 62.1 (2017): 49-73. <http://eudml.org/doc/287587>.

@article{Vaněk2017,
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.},
author = {Vaněk, Petr, Pultarová, Ivana},
journal = {Applications of Mathematics},
keywords = {nonlinear multigrid; exact interpolation scheme},
language = {eng},
number = {1},
pages = {49-73},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother},
url = {http://eudml.org/doc/287587},
volume = {62},
year = {2017},
}

TY - JOUR
AU - Vaněk, Petr
AU - Pultarová, Ivana
TI - Convergence theory for the exact interpolation scheme with approximation vector as the first column of the prolongator and Rayleigh quotient iteration nonlinear smoother
JO - Applications of Mathematics
PY - 2017
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 49
EP - 73
AB - 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.
LA - eng
KW - nonlinear multigrid; exact interpolation scheme
UR - http://eudml.org/doc/287587
ER -