--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/toolbox/fiedler.m	Wed May 06 14:56:53 2015 +0200
@@ -0,0 +1,33 @@
+function A = fiedler(c)
+%FIEDLER  Fiedler matrix - symmetric.
+%         A = FIEDLER(C), where C is an n-vector, is the n-by-n symmetric
+%         matrix with elements ABS(C(i)-C(j)).
+%         Special case: if C is a scalar, then A = FIEDLER(1:C)
+%                       (i.e. A(i,j) = ABS(i-j)).
+%         Properties:
+%           FIEDLER(N) has a dominant positive eigenvalue and all the other
+%                      eigenvalues are negative (Szego, 1936).
+%           Explicit formulas for INV(A) and DET(A) are given by Todd (1977)
+%           and attributed to Fiedler.  These indicate that INV(A) is
+%           tridiagonal except for nonzero (1,n) and (n,1) elements.
+%           [I think these formulas are valid only if the elements of
+%           C are in increasing or decreasing order---NJH.]
+
+%           References:
+%           G. Szego, Solution to problem 3705, Amer. Math. Monthly,
+%              43 (1936), pp. 246-259.
+%           J. Todd, Basic Numerical Mathematics, Vol. 2: Numerical Algebra,
+%              Birkhauser, Basel, and Academic Press, New York, 1977, p. 159.
+
+n = max(size(c));
+
+%  Handle scalar c.
+if n == 1
+   n = c;
+   c = 1:n;
+end
+
+c = c(:).';                    % Ensure c is a row vector.
+
+A = ones(n,1)*c;
+A = abs(A - A.');              % NB. array transpose.