function [A,b,x] = foxgood(n) %FOXGOOD Test problem: severely ill-posed problem. % % [A,b,x] = foxgood(n) % % This is a model problem which does not satisfy the % discrete Picard condition for the small singular values. % The problem was first used by Fox & Goodwin.  % Reference: C. T. H. Baker, "The Numerical Treatment of % Integral Equations", Clarendon Press, Oxford, 1977; p. 665.  % Discretized by simple quadrature (midpoint rule).  % Per Christian Hansen, IMM, 03/16/93.  % Initialization. h = 1/n; t = h*([1:n]' - 0.5);  A = h*sqrt((t.^2)*ones(1,n) + ones(n,1)*(t.^2)'); x = t; b = ((1+t.^2).^1.5 - t.^3)/3;