251 research outputs found
On the Convergence of Ritz Values, Ritz Vectors, and Refined Ritz Vectors
No full textThis paper concerns the Rayleigh--Ritz method for computing an approximation to an eigenpair (; x) of a non-Hermitian matrix A. Given a subspace W that contains an approximation to x, this method returns an approximation (; ~ x) to (; x). We establish four convergence results that hold as the deviation ffl of x from W approaches zero. First, the Ritz value converges to . Second, if the residual A~x \Gamma ~x approaches zero, then the Ritz vector ~ x converges to x. Third, we give a condition on the eigenvalues of the Rayleigh quotient from which the Ritz pair is computed that insures convergence of the Ritz vector. Finally, we show that certain refined Ritz vectors, introduced by the first author, converge unconditionally. This report is available by anonymous ftp from thales.cs.umd.edu in the directory pub/reports or on the web at http://www.cs.umd.edu/ stewart/. y Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P.R. China, ([email protected]..
Measurement of the electron's electric dipole moment using YbF molecules: methods and data analysis
No full text21.06.13 KB. Ok to add the author accepted version to spiral. IO
Einstein’s Investigations of Galilean Covariant Electrodynamics prior to 1905
No full textEinstein learned from the magnet and conductor thought experiments how to use field transformation laws to extend the covariance to Maxwell’s electrodynamics. If he persisted in his use of this device, he would have found that the theory cleaves into two Galilean covariant parts, each with different field transformation laws. The tension between the two parts reflects a failure not mentioned by Einstein: that the relativity of motion manifested by observables in the magnet and conductor thought experiment does not extend to all observables in electrodynamics. An examination of Ritz’s work shows that Einstein’s early view could not have coincided with Ritz’s on an emission theory of light, but only with that of a conveniently reconstructed Ritz. One Ritz-like emission theory, attributed by Pauli to Ritz, proves to be a natural extension of the Galilean covariant part of Maxwell’s theory that happens also to accommodate the magnet and conductor thought experiment. Einstein's famous chasing a light beam thought experiment fails as an objection to an ether-based, electrodynamical theory of light. However it would allow Einstein to formulate his general objections to all emission theories of light in a very sharp form. Einstein found two well known experimental results of 18th and19th century optics compelling (Fizeau’s experiment, stellar aberration), while the accomplished Michelson-Morley experiment played no memorable role. I suggest they owe their importance to their providing a direct experimental grounding for Lorentz’ local time, the precursor of Einstein’s relativity of simultaneity, and do it essentially independently of electrodynamical theory. I attribute Einstein’s success to his determination to implement a principle of relativity in electrodynamics, but I urge that we not invest this stubbornness with any mystical prescience
A simple and accurate mixed Ritz-DQM formulation for free vibration of rectangular plates involving free corners
No full textAbstractIt is well known that the classical global approximation methods such as the conventional Ritz method and the conventional differential quadrature method (DQM) have some difficulty in determining the natural frequencies of rectangular plates involving free corners. The mixed Ritz-DQM formulation, which has been recently developed by the present author, was also shown to have such difficulty. This is because it is very difficult to implement the free corner boundary condition in these methods. To overcome this difficulty, this paper presents a mixed Ritz-DQM formulation in which the free corner boundary condition is implemented in a simple and easy manner. First, we present a new scheme for implementing multiple boundary conditions in the DQM discretized equations. By the help of this scheme, we then show that the free corner boundary condition can also be easily implemented in the final matrix equations of the Ritz-DQM approach. Finally, we validate the effectiveness of the proposed approach through numerical experiments. Numerical results show the advantages of the proposed method over some versions of the DQM in terms of accuracy and performance
Maine places that appear in the fiction of native author Stephen King; including
No full textMaine places that appear in the fiction of native author Stephen King; including Lisbon High School and Worumbo Mill in Lisbon Falls, the Ritz in Lewiston, Food City in Bridgton, the Appalachian Trail, Bangor International Airport, and Orrington House
Accelerating the Induced Dimension Reduction method using spectral information
No full textThe Induced Dimension Reduction method (IDR(s)) (Sonneveld and van Gijzen, 2008) is a short-recurrences Krylov method to solve systems of linear equations. In this work, we accelerate this method using spectral information. We construct a Hessenberg relation from the IDR(s) residual recurrences formulas, from which we approximate the eigenvalues and eigenvectors. Using the Ritz values, we propose a self-contained variant of the Ritz-IDR(s) method (Simoncini and Szyld, 2010) for solving a system of linear equations. In addition, the Ritz vectors are used to speed-up IDR(s) for the solution of sequence of systems of linear equations.Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.Numerical Analysi
Birmingham News sleeve BN0071538
No full textGirls and moms that spent 19 hours in line to get New Kids [on the Block] tickets / With tickets are / Back row left to right / Gail King / Wendy Ritz / Front row left to right / Melissa Ritz 14 / Erin King, 13 / Take black and white also / 1112 Meadow Drive, apartments directly across 280 from Meadowbrook entrance. (Meadows on Lake Apartments) / Get shots of mothers, too, they stood in line as long as daughters / [Work order included
La sémantique de la négation en français
No full text4. M.-E. Ritz, « The semantics of negation in French »
This paper shows how the use of a metalanguage consisting of primitives allows one to clarify some of the problems raised by negation in French. The latter is envisaged not from a static point of view, but, within the psychomecanic tradition, as a cinetism moving from more to less, from plus to minus. The author deals first with fuzziness in negation as achieved by the use of hedges, then looks at the « redundant » ne wich occasionally occurs in the language.Ritz Marie-Ève. La sémantique de la négation en français. In: Langue française, n°98, 1993. Les primitifs sémantiques, sous la direction de Bert Peeters. pp. 67-78
Book Review: Hotel Ritz-Comparing Mexican and U.S. Street Prostitutes: Factors in HIV/AIDS Transmission and Book Review: Women's Experiences with HIV/AIDS: Mending Fractured Selves
No full textTitle: Hotel Ritz-Comparing Mexican and U.S. Street Prostitutes: Factors in HIV/AIDS Transmission
Author: David J. Bellis, Ph.D.
Reviewers: J. Gary Linn & Carol Bompart
Publisher: The Haworth Press, 2003
ISBN 0-7890-1776-8, 128 pp.
Cost: 20.00 US
ACCELERATING CONVERGENCE BY AUGMENTED RAYLEIGH-RITZ PROJECTIONS FOR LARGE-SCALE EIGENPAIR COMPUTATION
No full textIterative algorithms for large-scale eigenpair computation of symmetric matrices are mostly based on subspace projections consisting of two main steps: a subspace update (SU) step that generates bases for approximate eigenspaces, followed by a Rayleigh-Ritz projection step that extracts approximate eigenpairs. A predominant methodology for the SU step makes use of Krylov subspaces and builds orthonormal bases piece by piece in a sequential manner. On the other hand, block methods such as the classic (simultaneous) subspace iteration, allow higher levels of concurrency than what is reachable by Krylov subspace methods, but may suffer from slow convergence. In this work, we analyze the rate of convergence for a simple block algorithmic framework that combines an augmented Rayleigh-Ritz (ARR) procedure with the subspace iteration. Our main results are Theorem 4.5 and its corollaries, which show that the ARR procedure can provide significant accelerations to convergence speed. Our analysis will offer useful guidelines for designing and implementing practical algorithms from this framework.NSFC [11322109, 91330202, 11421101]; National Basic Research Project [2015CB856002]; NSF [DMS-1115950, DMS-1418724]SCI(E)ARTICLE2273-2963
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