Results 1 to 10 of about 6,337 (213)

On the stability of the Rayleigh–Ritz method for eigenvalues [PDF]

Numerische Mathematik, 2017
This article deals with the ratio \(\hat{\lambda}_k/\lambda_k\), where \(\hat{\lambda}_k\) (resp. \(\lambda_k\)) is the \(k\)th numerical eigenvalue using the Rayleigh-Ritz methods (resp. the \(k\)th exact eigenvalue of Laplace operator). It is shown that in the context of classical finite elements, the maximal ratio blows up with the polynomial degree.
Dietmar Gallistl, P. Huber, Daniel Peterseim   +2 more
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On the Methods of Rayleigh-Ritz-Weinstein [PDF]

Proceedings of the American Mathematical Society, 1952
The Rayleigh-Ritz-Weinstein methods are concerned with the connection between eigenvalues of a completely continuous symmetric operator in a Hilbert space and the eigenvalues of its projection into a subspace X of H such that the difference Hex-x is finitedimensional.
openaire   +1 more source

An analysis of the Rayleigh–Ritz method for approximating eigenspaces [PDF]

Mathematics of Computation, 2000
This paper concerns the Rayleigh–Ritz method for computing an approximation to an eigenspace X \mathcal {X}
Zhongxiao Jia, G. W. Stewart
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Convergence Rate Analysis for Deep Ritz Method

Communications in Computational Physics, 2022
Using deep neural networks to solve PDEs has attracted a lot of attentions recently. However, why the deep learning method works is falling far behind its empirical success. In this paper, we provide a rigorous numerical analysis on deep Ritz method (DRM) \cite{wan11} for second order elliptic equations with Neumann boundary conditions.
Duan, Chenguang, Jiao, Yuling, Lai, Yanming, Li, Dingwei, Lu, Xiliang, Yang, Jerry Zhijian   +5 more
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Food inflation pass‐through from agricultural imports in a small open economy

American Journal of Agricultural Economics, EarlyView.
Abstract This paper develops a new framework for quantifying cost pass‐through in a small open economy by estimating firm‐level markup responses to agricultural import price shocks. We show theoretically that markup adjustments depend on firms' reliance on imported inputs and demand curvature, generating heterogeneous inflationary effects across firm ...
Minseong Kang, Seungki Lee
wiley   +1 more source

Erste Hinweise auf Ozonido‐TMC‐Komplexe von Eisen und Kobalt

Angewandte Chemie, EarlyView.
Die Umsetzung der Eisen(II)‐Komplexe [(TMC)Fe(OTf)]BArF und [(D12‐TMC)Fe(OTf)]BArF sowie der Kobalt(II)‐Komplexe [(TMC)Co(OTf)]BArF und [(D12‐TMC)Co(X)]BArF (X = OTf, F) mit Ozon führt in einem 4:1‐Gemisch aus 2‐Me‐THF und THF bei Temperaturen bis −155°C zur Bildung von Ozonido‐ und Oxido‐Komplexen.
Stefan Schaub, Dennis Gerbig, Raffael C. Wende, Heike Hausmann, Jonathan Becker, Christian Würtele, Laura Senft, Ina Kellner, Gunasekaran Velmurugan, Marion Kerscher, Ivana Ivanović‐Burmazović, Peter Comba, Joshua Telser, Peter R. Schreiner, Siegfried Schindler   +14 more
wiley   +1 more source

On the Convergence of Ritz-Galerkin's Method

Publications of the Research Institute for Mathematical Sciences, 1968
where D is a bounded domain in the (#, jO -plane, P is the boundary of D, and 0), &(:>0), c(>0), / are smooth functions defined on D. In Ritz-Galerkin's method, first we choose a system of linearly independent functions {^J such that they satisfy the given homogeneous boundary condition and they are dense in a function space containing the exact ...
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A Short Theory of the Rayleigh–Ritz Method [PDF]

Computational Methods in Applied Mathematics, 2013
Abstract. We present some new error estimates for the eigenvalues and eigenfunctions obtained by the Rayleigh–Ritz method, the common variational method to solve eigenproblems. The errors are bounded in terms of the error of the best approximation of the eigenfunction under consideration by functions in the ansatz space.
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First Evidence for Ozonido‐TMC Complexes of Iron and Cobalt

Angewandte Chemie International Edition, EarlyView.
Reaction of ozone with iron(II) complexes [(TMC)Fe(OTf)]BArF, [(D12‐TMC)Fe(OTf)]BArF, and cobalt(II) complexes [(TMC)Co(OTf)]BArF, [(D12‐TMC)Co(X)]BArF (X = OTf, F) gives ozonido and oxido complexes at temperatures as low as –155°C in a 4:1 mixture of 2‐Me‐THF and THF. ABSTRACT We present compelling evidence for the first Fe‐ and Co‐ozonido complexes: [
Stefan Schaub, Dennis Gerbig, Raffael C. Wende, Heike Hausmann, Jonathan Becker, Christian Würtele, Laura Senft, Ina Kellner, Gunasekaran Velmurugan, Marion Kerscher, Ivana Ivanović‐Burmazović, Peter Comba, Joshua Telser, Peter R. Schreiner, Siegfried Schindler   +14 more
wiley   +1 more source

Estimates for the errors in the Rayleigh-Ritz method [PDF]

Pacific Journal of Mathematics, 1953
with homogeneous linear boundary conditions, denoted by (C). It is assumed that the parameter λ does not appear in the boundary conditions. The region R of the problem may be of any number of dimensions; the symbol ff(P)dP will mean an integral over /?, dP standing for the Euclidean volume element; (/, g) will stand for ff(P)g{P)dP; and ||/||, for (f ...
openaire   +2 more sources