Showing papers by "Albrecht Böttcher published in 2005"
TL;DR: In this paper, it was shown that the Frobenius norm of the commutator of two large matrices typically clusters sharply around a certain value, which is much smaller than one would predict.
64 citations
TL;DR: In this paper, two elementary derivations of the Toeplitz determinant generated by a pure Fisher-Hartwig singularity were presented. But neither of these derivations can be used to derive the determinant of the pure Fisher Hartwig determinant.
Abstract: We present two elementary derivations of the formula for the Toeplitz determinant generated by a pure Fisher-Hartwig singularity.
27 citations
TL;DR: The purpose of this note is to show that in this case the structured condition numbers do with high probability also increase exponentially, which supports the claim that one is not likely to win much on the average Toeplitz input by passing from the usual condition numbers of ToePlitz matrices to their structured counterparts.
Abstract: When working with structured matrices, structured condition numbers are more meaningful than usual condition numbers. The usual condition numbers of Toeplitz matrices may grow exponentially with the dimension of the matrix. The purpose of this note is to show that in this case the structured condition numbers do with high probability also increase exponentially, which supports the claim that one is not likely to win much on the average Toeplitz input by passing from the usual condition numbers of Toeplitz matrices to their structured counterparts. Copyright © 2004 John Wiley & Sons, Ltd.
12 citations