** Next:** Generalized Hermitian Eigenproblems
** Up:** Hermitian Eigenproblems J.
** Previous:** Related Eigenproblems
** Contents**
** Index**

##

Example

For the vibrating mass-spring system introduced in §2.1 and
Figure 2.1, we assume that

- all masses , so , and
- all damping constants , so .

This simplies the equations of motion to
.
We solve them by substituting
, where is
a constant vector and is a constant scalar to be determined.
This yields

Thus is an eigenvector
and is an eigenvalue of the symmetric positive
definite tridiagonal matrix . Thus is pure imaginary
and we get that is periodic with period
.
Symmetric tridiagonal matrices have particularly fast and efficient
eigenvalue algorithms.
Later sections deal with the cases of nonunit masses
and nonzero damping constants .

Susan Blackford
2000-11-20