Resolvent contours: The Resolvent matrix is = () − The diagrams below show the Resolvent contours / -pseudospectrum (() ) close to the origin of a low resolution Eigen spectrum. The contours are of the followi ng form: ()={∈ ∶ () ≤ }The contours in the diagram below represent = 1, 10 − , 10 −2 , 10 −3
The diagrams below show the Resolvent contours / -pseudospectrum
(()) close to the origin of a low resolution Eigen spectrum. The
contours are of the following form:
() = { ( ) }
The contours in the diagram below represent = 1, 101, 102,
103
This next diagram is a closer look at the diagram above
Zoom in version of the above diagram
The Eigenvalues that are farthest from the contours are the
eigenvalues that are the most susceptible
to disturbance. Therefore, the Eigenvalues closest to the
origin, represent the non-normal behavior
of the matrix.
Reasoning:
If is a matrix over . Then for () we have
( )1 1
(, ())
However, if is normal then,
( )1 =1
(, ())
NON-NORMAL BEHAVIOUR OF THE H MATRIX
Where,
(, ) = inf {| || }
Questions:
1. Please let me know if my interpretation of the Resolvent
contours and what they signify is
incorrect.
2. The contour program is sluggish, similar contours on higher
resolution Eigen-spectrum take
a lot longer. I wanted to know if you would like to see the same
program run for the high-res
