--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/pentoep.m	Thu May 07 18:36:24 2015 +0200
@@ -0,0 +1,26 @@
+function P = pentoep(n, a, b, c, d, e)
+%PENTOEP   Pentadiagonal Toeplitz matrix (sparse).
+%          P = PENTOEP(N, A, B, C, D, E) is the N-by-N pentadiagonal
+%          Toeplitz matrix with diagonals composed of the numbers
+%          A =: P(3,1), B =: P(2,1), C =: P(1,1), D =: P(1,2), E =: P(1,3).
+%          Default: (A,B,C,D,E) = (1,-10,0,10,1) (a matrix of Rutishauser).
+%                    This matrix has eigenvalues lying approximately on
+%                    the line segment 2*cos(2*t) + 20*i*sin(t).
+%
+%          Interesting plots are
+%          PS(FULL(PENTOEP(32,0,1,0,0,1/4)))  - `triangle'
+%          PS(FULL(PENTOEP(32,0,1/2,0,0,1)))  - `propeller'
+%          PS(FULL(PENTOEP(32,0,1/2,1,1,1)))  - `fish'
+
+%          References:
+%          R.M. Beam and R.F. Warming, The asymptotic spectra of
+%             banded Toeplitz and quasi-Toeplitz matrices, SIAM J. Sci.
+%             Comput. 14 (4), 1993, pp. 971-1006.
+%          H. Rutishauser, On test matrices, Programmation en Mathematiques
+%             Numeriques, Editions Centre Nat. Recherche Sci., Paris, 165,
+%             1966, pp. 349-365.
+
+if nargin == 1, a = 1; b = -10; c = 0; d = 10; e = 1; end
+
+P = spdiags([ a*ones(n,1) b*ones(n,1) c*ones(n,1) d*ones(n,1) ....
+              e*ones(n,1) ], -2:2, n, n);