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

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 inve...

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Vydané v:Applications of mathematics (Prague) Ročník 62; číslo 1; s. 49 - 73
Hlavní autori: Vank, Petr, Pultarová, Ivana
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Berlin/Heidelberg Springer Berlin Heidelberg 01.02.2017
Springer Nature B.V
Predmet:
Algorithms
Analysis
Applications of Mathematics
Approximation
Classical and Continuum Physics
Convergence
Eigenvalues
Eigenvectors
Estimates
Inverse
Iterative methods
Mathematical analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Nonlinearity
Nuclear reactors
Optimization
Quotients
Studies
Theoretical
nonlinear multigrid
exact interpolation scheme
65N55
ISSN:0862-7940, 1572-9109
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Shrnutí: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.
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ISSN:0862-7940
1572-9109
DOI:10.21136/AM.2017.0101-16