--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/prolate.m	Wed May 06 14:56:53 2015 +0200
@@ -0,0 +1,21 @@
+function A = prolate(n, w)
+%PROLATE   Prolate matrix - symmetric, ill-conditioned Toeplitz matrix.
+%          A = PROLATE(N, W) is the N-by-N prolate matrix with parameter W.
+%          It is a symmetric Toeplitz matrix.
+%          If 0 < W < 0.5 then
+%             - A is positive definite
+%             - the eigenvalues of A are distinct, lie in (0, 1), and
+%               tend to cluster around 0 and 1.
+%          W defaults to 0.25.
+
+%          Reference:
+%          J.M. Varah. The Prolate matrix. Linear Algebra and Appl.,
+%          187:269--278, 1993.
+
+if nargin == 1, w = 0.25; end
+
+a = zeros(n,1);
+a(1) = 2*w;
+a(2:n) = sin( 2*pi*w*(1:n-1) ) ./ ( pi*(1:n-1) );
+
+A = toeplitz(a);