foxgood.m

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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;