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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Volume extrapolation via eigenvector continuation

Here, we develop an extension of eigenvector continuation (EC) that makes it possible to extrapolate simulations of quantum systems in finite periodic boxes across large ranges of box sizes. The formal justification for this approach, which we call finite-volume eigenvector continuation (FVEC), is provided by matching periodic functions at different box sizes. As concrete FVEC implementation we use a discrete variable representation based on plane-wave states and present several applications calculated within this framework.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1978

Signature extraction of ocean pollutants by eigenvector transformation of remote spectra

Spectral signatures of suspended matter in the ocean are being extracted through characteristic vector analysis of remote ocean color data collected with MOCS (Multichannel Ocean Color Sensor). Spectral signatures appear to be obtainable through analyses of 'linear' clusters that appear on scatter diagrams associated with eigenvectors. Signatures associated with acid waste, sewage sludge, oil, and algae are presented. The application of vector analysis to two acid waste dumps overflown two years apart is examined in some detail. The relationships between eigenvectors and spectral signatures for these examples are analyzed. These cases demonstrate the value of characteristic vector analysis in remotely identifying pollutants in the ocean and in determining the consistency of their spectral signatures.

Grew, G. W.↗
NASA NTRS1981

Eigenvector determination by iterative optical methods

Three power algorithms are considered by which an iterative optical processor can be used to compute the eigenvalues and eigenvectors of a matrix. The algorithms are appropriate for three applications: (1) calculating the largest eigenvalue; (2) calculating the eigenvalues in order of decreasingly dominant eigenvalues; and (3) calculating the eigenvector whose eigenvalue is closest to a given value.

Vijaya Kumar, B. V. K.↗
NASA NTRS1989

Eigenvector derivatives of repeated eigenvalues using singular value decomposition

An explicit formula is obtained for the first-order eigenvector derivative that corresponds to the eigenvector of a repeated eigenvalue, in the case of the nonself-adjoint eigenvalue problem. This method applies to the class of nondefective problems whose first eigenvalue derivatives of the repeated eigenvalues are distinct. A singular-value decomposition approach is used to compute four requisite bases for eigenspaces, as well as to keep track of the dimensions of state variables and the conditioning of the state equations.

Lim, Kyong B.↗
NASA NTRS1992

A subspace iteration for eigenvector derivatives

An iterative procedure for calculating eigenvector derivatives has been developed based on the subspace iteration concept. The basic formulation is derived directly from the first variation of the resulting equations of subspace iteration for solving eigenvalue problems. Since the basic formulation conserves the convergence properties of the original subspace iteration for eigen-problems, an overrelaxation scheme similar to Bathe's approach is employed to accelerate the subspace iteration process for calculating eigenvector derivatives.

Ting, T.↗
NASA NTRS1994

Structural damage detection of space truss structures using best achievable eigenvectors

A method is presented by which measured modes and frequencies from a modal test can be used to determine the location and magnitude of damage in a space struss structure. The damage is located by computing the Euclidean distances between the measured mode shapes and the best achievable eigenvectors. The best achievable eigenvectors are the projection of the measured mode shapes onto the subspace defined by the refined analytical model of the structure and the measured frequencies. Loss of both stiffness and mass properties can be located and quantified. To examine the performance of the method when experimentally measured modes are employed, various damage detection studies using a laboratory eight-bay truss structure were conducted. The method performs well even though the measurement errors inevitably make the damage location more difficult.

Lim, Tae W.↗
DOE OSTI2022

Controlled precision QUBO-based algorithm to compute eigenvectors of symmetric matrices

We describe an algorithm to compute the extremal eigenvalues and corresponding eigenvectors of a symmetric matrix which is based on solving a sequence of Quadratic Binary Optimization problems. This algorithm is robust across many different classes of symmetric matrices; It can compute the eigenvector/eigenvalue pair to essentially any arbitrary precision, and with minor modifications, can also solve the generalized eigenvalue problem. Performance is analyzed on small random matrices and selected larger matrices from practical applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

The Eigenvector-Eigenvalue Identity and other pragmatic topics in linear algebra for physicists

Diagonalization of an Hermitian matrix is a common task in physics. All of us have diagonalized 2x2 matrices but few have diagonalized a 3x3 matrix algebraically except in special simplifying cases. In this colloquium, I will discuss the mathematics and methods for diagonalizing small, but larger than 2x2 marices, and discuss the recently rediscovered Eigenvector-Eigenvalue identity. As an explicit, pragmatic example I will use the propagation of neutrino's propagating through matter which is inherently a 3x3 problem.

Parke, Stephen [Fermilab] (ORCID:0000000320286782)↗
NASA NTRS1975

On eigenvectors of multiple eigenvalues obtained in NASTRAN

In the case of nonmultiple eigenvalues, each of the three real eigenvalue extraction methods available in NASTRAN will, for a given type of normalization, give essentially the same eigenvectors, but this is not so in the case of multiple eigenvalues. This discrepancy is explained and illustrated by considering the example of a NASTRAN demonstration problem that has both multiple and nonmultiple eigenvalues.

Pamidi, P. R.↗
NASA NTRS1978

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.↗