Big Chemical Encyclopedia

Chemical substances, components, reactions, process design ...

Articles Figures Tables About

Estimating eigenvalues Gershgorins theorem

With the significant effort required to find the roots of [Pg.111]

For matrices that are not triangular, we cannot determine the eigenvalues by inspection, but we can obtain upper and lower bounds using Gershgorin s theorem. Let be an iVx W [Pg.111]

Matrix norm, spectral radius, and condition number [Pg.113]

We have defined the norm of a vector as a rule that assigns to every v e a scalar w 9 that represents the size of v and that satisfies w 0, where w = 0 if and only if V = 0. For each particular vector norm v, we can generate a corresponding ia/nx norm,  [Pg.113]

As the maximum is attained when points in the direction of an eigenvector for the eigenvalue of largest modulus. [Pg.113]


The famous Gershgorin theorem gives estimates of eigenvalues. The estimates of correspondent eigenvectors are not so well-known. In the chapter we use some estimates of eigenvectors of kinetic matrices. Here we formulate and prove these estimates for general matrices. Below A = (a,y) is a complex n x n matrix. Pi — (sums of nondiagonal elements in rows), Qi — (sums of... [Pg.168]


See other pages where Estimating eigenvalues Gershgorins theorem is mentioned: [Pg.111]    [Pg.111]    [Pg.113]    [Pg.135]    [Pg.523]   


SEARCH



Eigenvalue

Estimability theorems

Gershgorin theorem

© 2024 chempedia.info