| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4603124 | Linear Algebra and its Applications | 2009 | 8 Pages |
Abstract
It is known, for example, that the eigenvalues of the N×N matrix A, arising in the discretization of the wave equation, whose only nonzero entries are Akk+1=Ak+1k=-1,k=1,…,N-1, and Akk=2,k=1,…,N, are 2{1-cos[pπ/(N+1)]} with corresponding eigenvectors v(p) given by . We show by considering a simple finite difference approximation to the second derivative and using the summation formulae for sines and cosines that these and other similar formulae arise in a simple and unified way.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
