Results 1 to 10 of about 5,798 (159)
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 +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.
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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 +5 more
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Business Strategy and the Environment, EarlyView.ABSTRACT We are interested in investigating whether firms use political donations as a license to neglect environmental sustainability. We further deepen the examination by exploring the role of executive contracting. Drawing on a wide range of data between 2002 and 2021 and a global sample, our findings confirm that firms use political contributions ...
Habiba Al‐Shaer +3 more
wiley +1 more source
International Journal of Cancer, EarlyView.Thyroid diseases are common among women of reproductive age and may be related to childhood cancer, but the evidence is inconsistent. This study of childhood cancer with maternal thyroid diseases and medication use in a population‐based case‐control study using Danish registries found positive associations between maternal goiter and overall cancer ...
Chuanjie Deng +5 more
wiley +1 more source
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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Psychology &Marketing, EarlyView.ABSTRACT Surprise marketing, characterized by unexpected tactics such as blind boxes and spontaneous discounts, captivates consumers by sparking curiosity and participation. Despite increasing industry use, scholarly research remains fragmented and limited.
Xin‐Jean Lim +2 more
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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 ...
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Movement Disorders, EarlyView.Abstract Background Long‐term exposure to air pollution has been linked to Parkinson's disease (PD) incidence, yet evidence is mixed, partly because of challenges with PD diagnosis and definition. We examined this association in a nationwide administrative cohort.
Thomas Cole‐Hunter +14 more
wiley +1 more source