Determination of viscoelastic spectra by matrix eigenvalue analysis

2002 ◽  
pp. 257-273 ◽  
Author(s):  
Ladislav Hanyk ◽  
Ctirad Matyska ◽  
David A. Yuen
Keyword(s):  
Eigenvalue Analysis ◽  
Matrix Eigenvalue

scholarly journals Pseudoinverse formulation of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem

2003 ◽  
Vol 2003 (9) ◽  
pp. 459-485
Author(s):  
Brian J. McCartin
Keyword(s):  
Perturbation Theory ◽  
Eigenvalue Problem ◽  
Symmetric Matrix ◽  
Comprehensive Treatment ◽  
Matrix Eigenvalue Problem ◽  
Degenerate Problem ◽  
Matrix Eigenvalue ◽  
Penrose Pseudoinverse ◽  
Schrödinger Perturbation

A comprehensive treatment of Rayleigh-Schrödinger perturbation theory for the symmetric matrix eigenvalue problem is furnished with emphasis on the degenerate problem. The treatment is simply based upon the Moore-Penrose pseudoinverse thus distinguishing it from alternative approaches in the literature. In addition to providing a concise matrix-theoretic formulation of this procedure, it also provides for the explicit determination of that stage of the algorithm where each higher-order eigenvector correction becomes fully determined. The theory is built up gradually with each successive stage appended with an illustrative example.

Real Asymmetric Matrix Eigenvalue Analysis for Dynamic Instability Problems

2000 ◽  
Author(s):  
Heewook Lee ◽  
Noboru Kikuchi
Keyword(s):  
Control Systems ◽  
Eigenvalue Problems ◽  
Dynamic Instability ◽  
Eigenvalue Analysis ◽  
Complex Eigenvalue ◽  
Friction Forces ◽  
Matrix Eigenvalue ◽  
Complex Eigenvalues ◽  
Complex Eigenvalue Analysis ◽  
Matrix Eigenvalue Problems

Abstract Complex eigenvalue analysis is widely used when the dynamic instability of the structure is in doubt due to friction forces, aerodynamic forces, control systems, or other effects. MSC/NASTRAN upper Hessenberg method and MATLAB eigenvalue solver produce fictitious nonzero real parts for real asymmetric matrix eigenvalue problems. For dynamic instability problems, since nonzero real parts of complex eigenvalues determine the unstable eigenvalues, the accuracy of real parts becomes crucial. The appropriate double shift QR or the QZ algorithms are applied to eliminate fictitious nonzero real parts and produce only authentic complex eigenvalues for real asymmetric matrix eigenvalue problems. Numerical examples are solved using the double shift QR and the QZ algorithms, and the results are compared with the results of MSC/NASTRAN upper Hessenberg method and MATLAB solvers.

scholarly journals A Note on the Eigenvalue Analysis of the SIMPLE Preconditioning for Incompressible Flow

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Shi-Liang Wu ◽  
Feng Chen ◽  
Xiao-Qi Niu
Keyword(s):  
Saddle Point ◽  
Incompressible Flow ◽  
Recent Article ◽  
Eigenvalue Analysis ◽  
Saddle Point Problems ◽  
Matrix Eigenvalue ◽  
Preconditioned Matrix ◽  
The Relationship ◽  
Generalized Saddle Point Problems

We consider the SIMPLE preconditioning for block two-by-two generalized saddle point problems; this is the general nonsymmetric, nonsingular case where the (1,2) block needs not to equal the transposed (2,1) block, and the (2,2) block may not be zero. The eigenvalue analysis of the SIMPLE preconditioned matrix is presented. The relationship between the two different formulations spectrum of the SIMPLE preconditioned matrix is established by using the theory of matrix eigenvalue, and some corresponding results in recent article by Li and Vuik (2004) are extended.

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Distance to SN 1987A and the LMC

1999 ◽  
Vol 190 ◽  
pp. 549-554
Author(s):  
Nino Panagia
Keyword(s):  
Angular Size ◽  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Light Curves ◽  
Distance Modulus ◽  
Absolute Size ◽  
Sn 1987A

Using the new reductions of the IUE light curves by Sonneborn et al. (1997) and an extensive set of HST images of SN 1987A we have repeated and improved Panagia et al. (1991) analysis to obtain a better determination of the distance to the supernova. In this way we have derived an absolute size of the ringRabs= (6.23 ± 0.08) x 1017cm and an angular sizeR″ = 808 ± 17 mas, which give a distance to the supernovad(SN1987A) = 51.4 ± 1.2 kpc and a distance modulusm–M(SN1987A) = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to bed(LMC) = 52.0±1.3 kpc, which corresponds to a distance modulus ofm–M(LMC) = 18.58±0.05.

International determination of the total motion of the pole

1961 ◽  
Vol 13 ◽  
pp. 29-41
Author(s):  
Wm. Markowitz
Keyword(s):  
Secular Motion ◽  
The Future

A symposium on the future of the International Latitude Service (I. L. S.) is to be held in Helsinki in July 1960. My report for the symposium consists of two parts. Part I, denoded (Mk I) was published [1] earlier in 1960 under the title “Latitude and Longitude, and the Secular Motion of the Pole”. Part II is the present paper, denoded (Mk II).

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

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