A Grcar matrix is a Toeplitz matrix with 1 on the main diagonal and the first few superdiagonals,
and 
on the first subdiagonal.
The usual choice of three superdiagonals gives
 |
(1)
|
for 
(Higham 1995, p. 46).
This is the transpose of the convention used by Grcar (1989, p. 54). For 
it is not a normal
matrix, making it useful for studying sensitivity of eigenvalues
and the behavior of iterative methods.
For 
, dots mark the eigenvalues,
and orange and blue curves bound the pseudospectra
for 
and 
, respectively. These contours are computed from
the smallest singular value of 
, using the spectral norm.
