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2.4.1 Largest Eigenvalue and Related Eigenvector
Regard the eigenvectors of
as the base vectors in -space. Then any -vector may be
written
with appropriate coefficients .
Let be the eigenvector corresponding to the largest
(by absolute value) eigenvalue .
Multiply several times by
, each time normalizing
the result:
After a few iterations
|
(2.5) |
To obtain the eigenvalue ,
use
where
is any cartesian component of the
unnormalized vector
.
EXAMPLE:
Let
and use
choose as the starting vector. The iterated and normalized
vectors are
From and the unnormalized
we find
.
The exact solution is
Next: 2.4.2 Arbitrary Eigenvalue/-vector: Inverse
Up: 2.4 Eigenvalues and Eigenvectors
Previous: 2.4 Eigenvalues and Eigenvectors
Franz J. Vesely Oct 2005
See also: "Computational Physics - An Introduction," Kluwer-Plenum 2001