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# foxgood

## (PublicToolbox/regutools/foxgood.m in BrainStorm 2.0 (Alpha))

### Function Synopsis

[A,b,x] = foxgood(n)

### Help Text

FOXGOOD Severely ill-posed testproblem.
[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.

### Listing of function C:\BrainStorm_2001\PublicToolbox\regutools\foxgood.m

function [A,b,x] = foxgood(n)
%FOXGOOD Severely ill-posed testproblem.
%
% [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, UNI-C, 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;

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