3 edition of Eigenvalue extraction in NASTRAN by the Tridiagonal Reduction (FEER) Method found in the catalog.
Eigenvalue extraction in NASTRAN by the Tridiagonal Reduction (FEER) Method
by National Aeronautics and Space Administration, For sale by the National Technical Information Service] in Washington, D.C, [Springfield, Va
Written in English
|Statement||Malcolm Newman and Paul F. Flanagan.|
|Series||NASA contractor report -- NASA CR-2731.|
|Contributions||Flanagan, Paul F., Analytical Mechanics Associates., Langley Research Center.|
|The Physical Object|
|Pagination||ix, 58 p. :|
|Number of Pages||58|
Yes. For general tridiagonal matrices, see The Numerical Recipes, Chap or Golub-Van Loan. For symmetric tridiagonal matrices, you can do better, see Coakley/Rochlin's paper.. Coakley, Ed S.; Rokhlin, Vladimir, A fast divide-and-conquer algorithm for computing the spectra of real symmetric tridiagonal matrices, Appl. Anal. 34, No. 3, (). The Symmetric Tridiagonal Eigenproblem has been the topic of some recent work. Many methods have been advanced for the computation of the eigenvalues of such a matrix. In this paper, we present a divide-and-conquer approach to the computation of the eigenvalues of a symmetric tridiagonal matrix via the evaluation of the characteristic by:
$\begingroup$ There are older questions on MO dealing with eigenvalues of symmetric tridiagonal; no closed form. You might want to ask on the scicomp stackexchange. $\endgroup$ – Suvrit May 23 . Eigenvalues computed using MAAX and KAAX matrices extracted from Nastran do not match the software's response. Complex eigenvalue extraction in NASTRAN by the tridiagonal reduction .
Installation - nastran command: fails with multiple X versions: Description: If V of n is installed in the same directory as V, then both cannot run. The intent was to allow users to use "nast" for V and "nast" or "nast" for V This feature was broken in the Vx releases. Avoidances: 1. In numerical linear algebra, the tridiagonal matrix algorithm, also known as the Thomas algorithm (named after Llewellyn Thomas), is a simplified form of Gaussian elimination that can be used to solve tridiagonal systems of equations.A tridiagonal system for n unknowns may be written as − + + + =, where = and. [⋱ ⋱ ⋱ −] [⋮] = [⋮].For such systems, the solution can be obtained.
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This document will discuss 3 of the commonly used eigenvalue extraction techniques used in NASTRAN: Modified Givens, Inverse, Lanczos.
In addition, 2 methods of automated model dynamic reduction will also be investigated: AUTOOMIT(static condensation or Guyan Reduction) and Generalized Dynamic Reduction.
Theversion of the Tridiagonal Reduction method reported on here is the one implementedin Level 16 of NASTRANfor real eigenvalue extraction in structural vibration and buckling problems.
The basic concepts underlying the method are summarizedonly briefly, since a more thorough exposition of the theoretical aspects are available in reference Size: KB.
This method is an automatic matrix reduction scheme whereby the eigensolutions in the neighborhood of a specified point in the eigenspectrum can be accurately extracted from a tridiagonal eigenvalue problem whose order is much lower than that of the full : P.
Flanagan and M. Newman. There are no files associated with this item. title: Real eigenvalue analysis in NASTRAN by the tridiagonal reduction (FEER) method. An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described.
As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size : M.
Newman and F. Mann. A new eigensolution routine, FEER (Fast Eigensolution Extraction Routine), used in conjunction with NASTRAN at Israel Aircraft Industries is described.
The FEER program is based on an automatic matrix reduction scheme whereby the lower modes of structures with many degrees of freedom can be accurately extracted from a tridiagonal eigenvalue problem whose size is of the same order of. LaBudde, The reduction of an arbitrary real square matrix to tridiagonal form using similarity transformations.
Mathematics of Computation (American Mathematical Society) 17 Author: K KadalbajooMohan, GuptaAnkit. The mathematical eigenvalue problem is a classical field of study, and much work has been devoted to providing eigenvalue extraction methods. Wilkinson's () book provides an excellent compendium on the problem.
The eigenvalue problems arising out of finite element models are a particular case: they involve large but usually narrowly banded matrices, and only a small number of eigenpairs are usually.
of order p, whose eigenvalues → λi. The proof of this theorem is fairly lengthy; see, for example, . The workload in the QL algorithm is O(n3) per iteration for a general matrix, which is prohibitive.
However, the workload is only O(n) per iteration for a tridiagonal matrix and O(n2) for a Hessenberg matrix, which makes it highly efﬁcient on these Size: 84KB. A cost-effective eigensolution method for large systems with Rockwell NASTRAN Eigenvalue extraction in zos steps, yielding the 23 accurate eigensolutions in the COSMIC/NASTRAN by the tridiagonal reduction frequency range 0 to 32 Hz, including three sets of (FEER) method, NASA CR (Aug.
double roots. Author: Viney K. Gupta, Joseph G. Cole, Wendell D. Mock. Eigenvalue extraction in NASTRAN by the tridiagonal reduction (FEER) method-real eigenvalue analysis. GOLUB and R. UNDERWOOD in Mathematical Software III Cited by: 5. Evaluation of Eigenvalue Routines for Large Scale Applications The NASA structural analysis (NASTRAN*) program is one of the most extensively (Givens' method), and tridiagonal reduction or.
The Tridiagonal Reduction or FEER Method is an automatic matrix reduction scheme whereby the eigensolutions in the neighborhood of a specified point in the eigenspectrum can be accurately extracted from a tridiagonal eigenvalue problem whose order. A tridiagonal matrix is a matrix which has nonzero elements only on the main diagonal and the first diagonal below and above it.
The Hessenberg decomposition of a selfadjoint matrix is in fact a tridiagonal decomposition. This class is used in SelfAdjointEigenSolver to compute the eigenvalues and eigenvectors of a selfadjoint matrix.
The fact that the Lanczos algorithm is coordinate-agnostic – operations only look at inner products of vectors, never at individual elements of vectors – makes it easy to construct examples with known eigenstructure to run the algorithm on: make a diagonal matrix with the desired eigenvalues on the diagonal; as long as the starting vector has enough nonzero elements, the algorithm will output a general tridiagonal symmetric matrix.
COMPLEX EIGENVALUE EXTRACTION IN NASTRAN BY THE TRIDIAGONAL REDUCTION (FEER) METHOD September NASA CR Malcolm Newman and Paul F. Flanagan Malcolm Newman and Paul F. Flanagan: EIGENVALUE EXTRACTION IN NASTRAN BY THE TRIDIAGONAL REDUCTION (FEER) METHOD - REAL EIGENVALUE ANALYSIS August NASA CR eigenvalue λ= b−2 √ ac).
The corresponding eigenvectors may be obtained from (10). Since j ≤n,wehave,ifwesetu1 =1,uj =(−ρ) j−1 when α= √ ac and uj = ρj−1 when α= − √ ac. 3 Special Tridiagonal Matrices Now we can apply the results of the last section to ﬁnd the eigenvalues of several tridiagonal matrices of the form (1).
EIGENVALUE EXTRACTION METHODS IN NASTRAN For real symmetric matrices there are four meth ods of eigenvalue extraction available in NAS TRAN: the determinant method, the inverse power method with shifts, the Givens' method of tridiagonalization, and the tridiagonal reduction or.
Eigenvalues of tridiagonal matrix using Strum Sequence and Gerschgorin theorem study the changes in sign in the sequences and find the eigenvalues. The reduction to a tridiagonal form is achieved by using the orthogonal transformation. Suppose the orthogonal books File Size: 68KB.
A New O(n2) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem by Inderjit Singh Dhillon Doctor of Philosophy in Computer Science University of California, Berkeley Professor James W. Demmel, Chair Computing the eigenvalues and orthogonal eigenvectors of an n ×n symmetric tridiagonal.
Properties. A tridiagonal matrix is a matrix that is both upper and lower Hessenberg matrix. In particular, a tridiagonal matrix is a direct sum of p 1-by-1 and q 2-by-2 matrices such that p + q/2 = n — the dimension of the tridiagonal. Although a general tridiagonal matrix is not necessarily symmetric or Hermitian, many of those that arise when solving linear algebra problems have one of.The Unsymmetric Tridiagonal Eigenvalue Problem Abstract The development of satisfactory methods for reducing an unsymmetric matrix to tridiagonal form has been greatly hampered by the fact that there is not an accepted good algorithm for exploiting this form.
Nevertheless, recently, promising elimination.TRIDIAGONAL TOEPLITZ MATRICES 1 Table I. Deﬁnitions of sets used in the paper. T the subspace of C n× formed by tridiagonal Toeplitz matrices N the algebraic variety of normal matrices in C n× NT N ∩T M the algebraic variety of matrices in C n× with multiple eigenvalues MT M∩T grows exponentially with the ratio of the absolute values of the sub- and super-diagonal.