Provides the Julia function
nrange(A; nk = 1, thmax = 32, noplot = false)
which evaluates and plots the numerical range of the
nk largest leading principal submatrices of A, using thmax
equally spaced angles in the complex plane.
The defaults are nk = 1 and thmax = 32.
The eigenvalues of A are plotted as x. The function returns f and e,
where f is the numerical range and e is a vector of eigenvalues of A.
Setting noplot = true suppresses the plot.
This function is a direct translation of fv.m in Professor Nick Higham's Matrix Computation Toolbox,
based on an original routine by A. Ruhe.
References:
- R. A. Horn and C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991; sec. 1.5.
- A. S. Householder, The Theory of Matrices in Numerical Analysis, Blaisdell, New York, 1964; sec. 3.3.
- C. R. Johnson, Numerical determination of the field of values of a general complex matrix, SIAM J. Numer. Anal., 15 (1978), pp. 595-602.
