%
% (Classical) Polynomial Interpolation
%

clear;

x = [ 0; 1; -1; 2; -2];
f = [ -5; -3; -15; 39; -9];
z = [ 3 ];

p = AitkenNeville( x, f, z );

a = NewtIntPol( x, f, 1 );
p = NewtIntPolEval( x, a, z )

clear;

x = [ 0; 1; 3; 2; 5];
f = [ 2; 1; 5; 6;-183];
z = [ 4 ];

p = AitkenNeville( x, f, z );

a = NewtIntPol( x, f, 1 );
p = NewtIntPolEval( x, a, z )

clear;

x = [ 0; 1; 3; 5; 8; 2];
f = [ 2; 3; 5; 7; 9;10];
z = [ 4 ];



p = AitkenNeville( x, f, z );

a = NewtIntPol( x, f, 1 );
p = NewtIntPolEval( x, a, z )


clear;
% Interpolation of Si(x) = int_0^x sin(t)/t dt 

x = [ 0; 0.1; 0.2; 0.3; 0.4; 0.5; 0.6; 0.7; 0.8; 0.9; 1.0];
f = [ 0.0; 0.0999; 0.1996; 0.2985; 0.3965; 0.4931; 0.5881; 0.6812; 0.7721; 0.8605; 0.9461];
z = [0.05; 0.25; 0.55; 0.75; 0.95; 1.5];
p = AitkenNeville( x, f, z );

a = NewtIntPol( x, f, 1 );
p = NewtIntPolEval( x, a, z )



%
% Hermite Interpolation
%

clear;

% Examples from Stoer/Bulirsch

x = [ 0; 0; 1; 1; 1];
f = [ -1; -2;  0; 10; 40];

a = HermiteInt( x, f )

x = [ 0; 0; 0; 2; 3; 3];
f = [ 1; 0;-1; 0; 2;-1];

a = HermiteInt( x, f )