Physics – Mathematical Physics
Scientific paper
2009-06-03
Physics
Mathematical Physics
Scientific paper
This note starts from work done by Dai, Geary, and Kadanoff (Hui Dai, Zachary Geary, and Leo P. Kadanoff, H. Dai, Z. Geary and L. P. Kadanoff, Journal of Statistical Mechanics, P05012 (2009)) on exact eigenfunctions for Toeplitz operators. It builds methods for finding convergent expansions for eigenvectors and eigenvalues of large-n Toeplitz matrices, using the infinite-n case as a starting point. One expansion is derived from operator equations having a two-dimensional continuous spectrum of eigenvalues, which include the eigenvalues of the finite-$n$ matrices. Another expansion is derived from the transpose equations, which have no eigenvalues at all. The two expansions work together to give an apparently convergent expansion with an expansion parameter expressed as an inverse power of n. A variational principle is developed which gives an approximate expression for determining eigenvalues. A consistency condition is generated, which gives to lowest order exactly the same condition for the eigenvalue.
No associations
LandOfFree
Expansions for Eigenfunction and Eigenvalues of large-n Toeplitz Matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Expansions for Eigenfunction and Eigenvalues of large-n Toeplitz Matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Expansions for Eigenfunction and Eigenvalues of large-n Toeplitz Matrices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-194439