How long does it take to compute the eigenvalues of a random symmetric matrix?

Details How long does it take to compute the eigenvalues of a random symmetric matrix? How long does it take to compute the eigenvalues of a random symmetric matrix?

2012-03-21

arxiv.org/abs/1203.4635v1

Mathematics

Numerical Analysis

16 Figures

Scientific paper

We present the results of an empirical study of the performance of the QR and Toda eigenvalue algorithms on random symmetric matrices. The random matrices are chosen from six ensembles, four of which lie in the Wigner class. We observe a form of universality for the deflation time statistics for random matrices within the Wigner class: for these ensembles, the empirical distribution of a normalized deflation time is found to collapse onto a curve that depends only on the algorithm, but not on the matrix size or deflation tolerance provided the matrix size is large enough (see Figure 3 and Figure 6). We also provide a quantitative statistical picture of the accelerated convergence of the shifted QR algorithm.

Affiliated with

Also associated with

No associations

Rating

How long does it take to compute the eigenvalues of a random symmetric matrix? 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 How long does it take to compute the eigenvalues of a random symmetric matrix?, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and How long does it take to compute the eigenvalues of a random symmetric matrix? will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-487854