On the approximation numbers of large Toeplitz matrices
Albrecht Böttcher · Documenta Mathematica · 1997
The k th approximation number s_k^{(p)}(A_n) of a complex n \times n matrix A_n is defined as the distance of A_n to the n \times n matrices of rank at most n-k . The distance is measured in the matrix norm associated with the l^p norm (1 on \mathbf C^n . In the case p=2 , the approximation numbers coincide with the singular values.