Results 191 to 200 of about 1,668 (228)

On the Numerical Stability of the Rayleigh–Ritz Method

SIAM Journal on Numerical Analysis, 1977
The numerical stability of the Rayleigh–Ritz method is investigated from the point of view of Mikhlin stability and of the condition number of the Rayleigh–Ritz matrix, and it is shown that the condition number approach is more appropriate for floating-point computation.
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Dynamic Condition Estimation and Rayleigh–Ritz Approximation

SIAM Journal on Matrix Analysis and Applications, 1994
The Rayleigh-Ritz approximation method is applied to dynamic condition estimation. It is used as a common framework from which many condition estimators can be viewed. This framework leads to natural generalizations of existing dynamic condition estimators as well as more convenient alternatives. Some numerical examples are provided.
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Some multipoint extensions of the Rayleigh–Ritz inequality

Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 1985
SynopsisWe obtain the best constants for multipoint extensions of the Rayleigh–Ritz inequality, and use our results to find good upper bounds for the constants involved in the standard spline approximation and interpolation error bound theory.
Brown, Richard C., Vrkoc, Ivo
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Rayleigh-Ritz Method

2013
This is the first of two chapters devoted to the approximate analysis of continuous systems. In this chapter, a global method of approximation is considered: the Rayleigh-Ritz method. It is based on the definition of a set of global assumed modes defined on the entire domain and satisfying the kinematic boundary conditions.
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On the Rayleigh-Ritz method

Journal of Mathematical Chemistry
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A Rayleigh-Ritz Autoencoder

2023 IEEE International Instrumentation and Measurement Technology Conference (I2MTC), 2023
Anika Terbuch, Paul O'Leary, Dimitar Ninevski, Elias Jan Hagendorfer, Elke Schlager, Andreas Windisch, Christoph Schweimer   +6 more
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Exploring the Rayleigh-Ritz Variational Principle

Journal of Chemical Education, 1998
The particle-in-a-box (PIB) system is used as a simple example in order to illustrate the basis of the quantum variational principle. After the general exposition of the variational principle demonstration, a quadratic polynomial trial function is applied to the PIB hamiltonian and the different steps of the demonstration are followed and reproduced ...
Emili Besalú, Josep Martí
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A moment equation reformulation of Rayleigh - Ritz theory

Journal of Physics A: Mathematical and General, 1996
Summary: We present a moment equation Rayleigh-Ritz (RR) variational theory for the ground-state energy. An extended Fourier transform space can be defined through the moment equation corresponding to a given Schrödinger Hamiltonian. Within this extended space, we can implement a variational ansatz with respect to configurations of the form ...
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Successive Approximations by the Rayleigh-Ritz Variation Method

Physical Review, 1933
Approximate eigenvalues given by the Rayleigh-Ritz variation method for handling linear differential equations are examined and relations are established between the discrete eigenvalues obtained in successive approximations. These relations should be of use in practical computations.
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The Rayleigh-Ritz and Trefftz Methods

1981
The Rayleigh-Ritz method belongs to the so-called direct methods of the calculus of variations, inasmuch as it is applied to problems formulated in an integral rather than a conventional, that is, differential, form. More often than not, the procedure involves the minimization of integrals containing unknown functions and their derivatives, without ...
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