[Master Index] [Index for PublicToolbox/regutools]

# 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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