Journal ArticleDOI
Simplified calculation of eigenvector derivatives
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A simplified procedure is presented for the determination of the derivatives of eigenvectors of nth order algebraic eigensystems, applicable to symmetric or nonsymmetric systems, and requires knowledge of only one eigenvalue and its associated right and left eigenavectors.Abstract:
A simplified procedure is presented for the determination of the derivatives of eigenvectors of nth order algebraic eigensystems. The method is applicable to symmetric or nonsymmetric systems, and requires knowledge of only one eigenvalue and its associated right and left eigenvectors. In the procedure, the matrix of the original eigensystem of rank (/?-!) is modified to convert it to a matrix of rank /?, which then is solved directly for a vector which, together with the eigenvector, gives the eigenvector derivative to within an arbitrary constant. The norm of the eigenvector is used to determine this constant and complete the calculation. The method is simple, since the modified n rank matrix is formed without matrix multiplication or extensive manipulation. Since the matrix has the same bandedness as the original eigensystems, it can be treated efficiently using the same banded equation solution algorithms that are used to find the eigenvectors.read more
Citations
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Modal sensitivities for repeated eigenvalues and eigenvalue derivatives
Jinsiang Shaw,Suhada Jayasuriya +1 more
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Automatic camera calibration for a multiple-sensor integrated coordinate measurement system
Tzung-Sz Shen,Chia-Hsiang Menq +1 more
TL;DR: An automatic camera calibration scheme that utilizes a coordinate measuring machine (CMM) and a camera calibration algorithm to calibrate camera parameters in three stages without nonlinear minimization procedures is presented for a multiple-sensor integrated coordinate measurement system.
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Eigensensitivity computation of asymmetric damped systems using an algebraic approach
TL;DR: In this paper, an algebraic method is presented for simultaneous computation of the derivatives of eigenvalues and those of their associated right and left eigenvectors, for asymmetric damped systems.
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Metric Optimization for Surface Analysis in the Laplace-Beltrami Embedding Space
Yonggang Shi,Rongjie Lai,Danny J.J. Wang,Daniel Pelletier,David C. Mohr,Nancy L. Sicotte,Arthur W. Toga +6 more
TL;DR: A novel approach for the intrinsic mapping of anatomical surfaces and its application in brain mapping research using the Laplace-Beltrami eigen-system, which realizes surface deformation in the embedding space via the iterative optimization of a conformal metric without explicitly perturbing the surface or its embedding.
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Universal three-body recombination via resonant d-wave interactions
TL;DR: In this paper, a generalized version of this Efimov scenario was studied, where two of the atoms were about to form a two-body $d$-wave dimer, resulting in strong $d-wave interactions, and the signature of such a universal three-body state was signaled experimentally by an enhancement of the three body recombination rate.
References
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Book
The algebraic eigenvalue problem
TL;DR: Theoretical background Perturbation theory Error analysis Solution of linear algebraic equations Hermitian matrices Reduction of a general matrix to condensed form Eigenvalues of matrices of condensed forms The LR and QR algorithms Iterative methods Bibliography.
Journal ArticleDOI
Rates of change of eigenvalues and eigenvectors.
R. L. Fox,M. P. Kapoor +1 more
TL;DR: Exact expressions for rates of change of eigenvalues and eigenvector to facilitate computerized design of complex structures are presented.
Journal ArticleDOI
Statistical Identification of Structures
TL;DR: In this paper, a method is formulated for systematically using experimental measurements of the natural frequencies and mode shapes of a structure to modify stiffness and mass characteristics of a finite element model, and an additional feature is that the engineer's confidence in the modeling of the various finite elements is quantified and incorporated into the revision procedure.
Journal ArticleDOI
Handbook for Automatic Computation. Vol II, Linear Algebra
James Hardy Wilkinson,C. Reinsch +1 more
TL;DR: Haida gwaii tourism guide, Handbook of raman spectroscopy, and the Jordan form, Kronecker's form for matrix pencils, and various condition in the Handbook.