Results 181 to 190 of about 244,383 (211)
Some of the next articles are maybe not open access.
BIT Numerical Mathematics, 2003
The authors investigate the conditions under which it is possible to estimate and compute error bounds on a computed eigenvector of a finite matrix. It is shown that nontrivial error bounds on an eigenvector are computable if and only if its geometric multiplicity is one. They also provide an algorithm for the computation of these error bounds and show
Rump, Siegfried M., Zemke, Jens-Peter M.
openaire +1 more source
The authors investigate the conditions under which it is possible to estimate and compute error bounds on a computed eigenvector of a finite matrix. It is shown that nontrivial error bounds on an eigenvector are computable if and only if its geometric multiplicity is one. They also provide an algorithm for the computation of these error bounds and show
Rump, Siegfried M., Zemke, Jens-Peter M.
openaire +1 more source
Extended eigenvalue–eigenvector method
Statistics & Probability Letters, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kataria, K. K., Khandakar, M.
openaire +2 more sources
2007
Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space.
openaire +1 more source
Eigenvalues and the associated eigenvectors of an endomorphism of a vector space are defined and studied, as is the spectrum of an endomorphism. The characteristic polynomial of a matrix is considered and used to define the characteristic polynomial of the endomorphism of a finitely-generated vector space.
openaire +1 more source
2009
Radiative flux transfer between Lambertian surfaces can be described in terms of linear resistive networks with voltage sources. This thesis examines how these "radiative transfer networks" provide a physical interpretation for the eigenvalues and eigenvectors of form factor matrices. This leads to a novel approach to photorealistic image synthesis and
openaire +1 more source
Radiative flux transfer between Lambertian surfaces can be described in terms of linear resistive networks with voltage sources. This thesis examines how these "radiative transfer networks" provide a physical interpretation for the eigenvalues and eigenvectors of form factor matrices. This leads to a novel approach to photorealistic image synthesis and
openaire +1 more source
1997
Gaussian elimination plays a fundamental role in solving a system Ax = b of linear equations. In order to solve a system of linear equations, Gaussian elimination reduces the augmented matrix to a (reduced) row-echelon form by using elementary row operations that preserve row and null spaces.
Jin Ho Kwak, Sungpyo Hong
openaire +1 more source
Gaussian elimination plays a fundamental role in solving a system Ax = b of linear equations. In order to solve a system of linear equations, Gaussian elimination reduces the augmented matrix to a (reduced) row-echelon form by using elementary row operations that preserve row and null spaces.
Jin Ho Kwak, Sungpyo Hong
openaire +1 more source
An eigenvector variability plot
2009Summary: Principal components analysis is perhaps the most widely used method for exploring multivariate data. We propose a variability plot composed of measures on the stability of each eigenvector over samples as a data exploration tool. We also show that this variability measure gives a good measure on the intersample variability of eigenvectors ...
Tu, I. P., Chen, H., Chen, X.
openaire +1 more source
Eigenvalue-Eigenvector Solution
1985In this chapter, methods are presented for solving the free vibration equation for a multi-degree of freedom system. This equation is called the eigenvalue equation. Its solution not only gives the natural frequencies and mode shapes but also allows the set of coupled equations representing the dynamic response of a system to be uncoupled and hence ...
openaire +1 more source