Structured condition numbers of large Toeplitz matrices are rarely better than usual condition numbers
Albrecht Böttcher, Sergei M. Grudsky · Numerical Linear Algebra with Applications · 2004
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.