Add core/hess_orth.

Author: higham

core/private/Contents.m

@@ -14,6 +14,7 @@
 %   gfpp       - Matrix giving maximal growth for Gaussian elim. with pivoting.
 %   hessfull01 - Totally nonnegative lower Hessenberg Toeplitz matrix.
 %   hessmaxdet - Upper Hessenberg matrix with maximal determinant.
+%   hess_orth  - Lower Hessenberg matrix with orthogonal columns.
 %   hess_sublu - Upper Hessengerg matrix giving subnormal numbers in LU factor.
 %   indef      -  Symmetric indefinite matrix with known inertia.
 %   kms_nonsymm - Nonsymmetric Kac-Murdock-Szego Toeplitz matrix.

core/private/hess_orth.m

@@ -0,0 +1,17 @@
+function [A,properties] = hess_orth(n)
+%HESS_ORTH   Lower Hessenberg matrix with orthogonal columns.
+%   A = HESS_ORTH(n) is an n-by-n lower Hessenberg matrix with
+%   integer elements and orthogonal columns.
+
+%   Reference: 
+%   S. K. Godunov, A. G. Antonov, O. P. Kiriljuk, and V. I. Kostin,
+%   Guaranteed Accuracy in Numerical Linear Algebra,
+%   Kluwer Academic Publishers, Dordrecht, The Netherlands, 1993, p. 480.
+
+properties = {'hessenberg', 'integer'};
+if nargin == 0, A = []; return, end
+
+A = tril(ones(n));
+for j = 1:n-1
+    A(j,j+1) = -(n-j);
+end

readme.md

@@ -25,6 +25,7 @@ The following matrices have been added since v1.0.
 - core/circul_binom
 - core/collatz
 - core/cross
+- core/hess_orth
 - core/hess_sublu
 - core/indef
 - core/milnes