--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/parter.m	Thu May 07 18:36:24 2015 +0200
@@ -0,0 +1,18 @@
+function A = parter(n)
+%PARTER    Parter matrix - a Toeplitz matrix with singular values near PI.
+%          PARTER(N) is the matrix with (i,j) element 1/(i-j+0.5).
+%          It is a Cauchy matrix and a Toeplitz matrix.
+
+%          At the Second SIAM Conference on Linear Algebra, Raleigh, N.C.,
+%          1985, Cleve Moler noted that most of the singular values of
+%          PARTER(N) are very close to PI.  An explanation of the phenomenon
+%          was given by Parter; see also the paper by Tyrtyshnikov.
+%
+%          References:
+%          The MathWorks Newsletter, Volume 1, Issue 1, March 1986, page 2.
+%          S.V. Parter, On the distribution of the singular values of Toeplitz
+%               matrices, Linear Algebra and Appl., 80 (1986), pp. 115-130.
+%          E.E. Tyrtyshnikov, Cauchy-Toeplitz matrices and some applications,
+%               Linear Algebra and Appl., 149 (1991), pp. 1-18.
+
+A = cauchy( (1:n)+0.5, -(1:n) );