Bounds for the eigenvalues of a simply- supported rectangular plate under a compressive stress varying linearly in the direction of loading
Upper bounds of eigenvalues of simply-supported rectangular plate using Rayleigh-Ritz method
Fauconneau, G.↗
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Generalized Rayleigh methods with applications to finding eigenvalues of large matrices
Generalized Rayleigh quotients for calculating eigenvalues and eigenvectors of large matrices
Vandergraft, J. S.↗
Triangular decomposition as an aid in determining eigenvalues of large-order banded symmetric matrices
Triangular decomposition as aid in determining eigenvalues of large-order banded symmetric matrices
Puccinelli, E. F.↗
Localization of the eigenvalues of linear integral equations with applications to linear ordinary differential equations
Localization of linear integral equation eigenvalues with applications to linear ordinary differential equations
Kranzler, S. K.↗
Noniterative solutions of integral equations for scattering. IV - Preliminary calculations for coupled open channels and coupled eigenvalue problems
Noniterative homogeneous solutions of integral equations for coupled open channel and coupled eigenvalue scattering
Kouri, D. J.↗
ALLMAT - A TSS/360 FORTRAN 4 subroutine for eigenvalues and eigenvectors of a general complex matrix
Subroutine ALLMAT for eigenvalues and eigenvectors of general complex nature
Fair, G.↗
Symbolic-numeric eigenvalue problems in quantum mechanics
Discussing problem of symbolic numeric conversion in solving quantum mechanical eigenvalue problems with FORMAC
Hartt, K.↗
The effect of local modifications on the eigenvalues and eigenvectors of damped linear systems
Discrete linear vibration systems viscous damping local modifications effect on eigenvalues and vectors, using Weissenburgers procedure in matrix form
Pomazal, R. J.↗
Extreme eigenvalues of Toeplitz matrices associated with certain orthogonal polynomials
Extreme eigenvalues of Toeplitz matrices associated with Laguerre and Jacobi polynomials, using finite difference operators
Baxley, J. V.↗
Eigenvalue properties of structural mean-axis systems
The authors review some of the properties of the pseudoinverse and oblique pseudoinverse of a linear transformation T from one finite-dimensional inner-product space into another, and then use these properties and a theorem of Milne (1968), which states that the oblique pseudoinverse can be expressed in terms of a weak generalized inverse and two projection operators, in order to compute a mean-axis influence coefficient matrix for the dynamic analysis of an elastic body. Some eigenvalue invariance properties of the mean-axis structural dynamics equations are demonstrated, and on the simple example of a uniform beam, it is shown that the finite frequencies and mode shapes of the mean axis structural system are identical to the nonzero frequencies and mode shapes of the free structure.
Cavin, R. K., III↗
CAVE3: A general transient heat transfer computer code utilizing eigenvectors and eigenvalues
The method of solution is a hybrid analytical numerical technique which utilizes eigenvalues and eigenvectors. The method is inherently stable, permitting large time steps even with the best of conductors with the finest of mesh sizes which can provide a factor of five reduction in machine time compared to conventional explicit finite difference methods when structures with small time constants are analyzed over long time periods. This code will find utility in analyzing hypersonic missile and aircraft structures which fall naturally into this class. The code is a completely general one in that problems involving any geometry, boundary conditions and materials can be analyzed. This is made possible by requiring the user to establish the thermal network conductances between nodes. Dynamic storage allocation is used to minimize core storage requirements. This report is primarily a user's manual for CAVE3 code. Input and output formats are presented and explained. Sample problems are included which illustrate the usage of the code as well as establish the validity and accuracy of the method.
Palmieri, J. V.↗
A simultaneous coordinate relaxation algorithm for large, sparse matrix eigenvalue problems
An algorithm is proposed for a scheme of simultaneous coordinate relaxation. A variant of root-shifting coordinate relaxation, this procedure consists of iterating several vectors at the same time, instead of one at a time. Results of application of the algorithm to test matrices are discussed. For many matrix eigenvalue problems for which coordinate relaxation is a viable approach, the present algorithm is more effective than previous implementations of coordinate relaxation. Total central processor operations should be decreased due to significantly improved convergence.
Raffenetti, R. C.↗
Graph theory approach to the eigenvalue problem of large space structures
Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.
Reddy, A. S. S. R.↗
Legendre-Tau approximation for functional differential equations. Part 3: Eigenvalue approximations and uniform stability
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A charactristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Ito, K.↗
The eigenvalues of the pseudospectral Fourier approximation to the operator sin (2x) d/dx
It is shown that the eigenvalues Z sub i of the pseudospectral Fourier approximation to the operator sin(2x) curly d/curly dx satisfy (R sub e) (Z sub i) = + or - 1 or (R sub e)(Z sub I) = 0. Whereas this does not prove stability for the Fourier method, applied to the hyperbolic equation U sub t = sin (2x)(U sub x) - pi x pi; it indicates that the growth in time of the numerical solution is essentially the same as that of the solution to the differential equation.
Tal-Ezer, H.↗
Eigenvalues and stability problems of rotors
The essential theoretical results of the application of a developed transfer matrix method to the free transverse vibration of a rotor are shown. Gyroscopic and shear effects, rotary inertia, and external and internal damping as well as the influence of sleeve bearings and rotor supports are taken into consideration. The eigenvalues of the motion equations of the rotor are searched by using a modified determinant method.
Walczyk, Z.↗
Control of large flexible systems via eigenvalue relocation
For the vibration control of large flexible systems, a control scheme by which the eigenvalues of the closed-loop systems are assigned to predetermined locations within the feasible region through velocity-only feedback is presented. Owing to the properties of second-order lambda-matrices and an efficient model decoupling technique, the control scheme makes it possible that selected modes are damped with the rest of the modes unchanged.
Denman, E. D.↗
Legendre-tau approximation for functional differential equations. III - Eigenvalue approximations and uniform stability
The stability and convergence properties of the Legendre-tau approximation for hereditary differential systems are analyzed. A characteristic equation is derived for the eigenvalues of the resulting approximate system. As a result of this derivation the uniform exponential stability of the solution semigroup is preserved under approximation. It is the key to obtaining the convergence of approximate solutions of the algebraic Riccati equation in trace norm.
Ito, K.↗