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Laborator SD

http://geeksquiz.com/binary-search-tree-set-2-delete/


MN:
Neville:

function [yi, P] = neville(x, y, xi)

n = length(x);
yi = zeros(1, length(xi));
P = zeros(n, n);
P(:, 1) = y;

for k = 1 : length(xi)
    for i = 1 : n - 1
        for j = 1 : (n - i)
            P(j, i + 1) = ((xi(k) - x(j)) * P(j + 1, i) + (x(j + i) - xi(k)) * P(j, i))/(x(j + i) - x(j));
        end
    end

    yi(k) = P(1, n);

end

end


Natural Spline:

function [s0,s1,s2,s3]=cubic_spline(x,y)

n = length(x);

h = x(2:n) - x(1:n-1);
d = (y(2:n) - y(1:n-1))./h;

lower = h(1:end-1);
main  = 2*(h(1:end-1) + h(2:end));
upper = h(2:end);
if n==2
    m=0;
else
T = spdiags([lower main upper], [-1 0 1], n-2, n-2);
rhs = 6*(d(2:end)-d(1:end-1));

m = T\rhs;
end

% Use natural boundary conditions where second derivative
% is zero at the endpoints

m = [ 0; m; 0];

s0 = y;
s1 = d - h.*(2*m(1:end-1) + m(2:end))/6;
s2 = m/2;
s3 =(m(2:end)-m(1:end-1))./(6*h);

end

Plot Natural Spline:

function yy = plot_cubic_spline(x,y,xx)

n = length(xx);
[s0, s1, s2, s3] = naturalspline(x', y');
yy = zeros(1, n);
for j = 1 : n
    for k = 1 : length(x)
        if xx(j) < x(k)
            break;
        end
    end

    i = k - 1;

    yy(j) = s0(i) + s1(i) * (xx(j) - x(i)) + s2(i) * (xx(j) - x(i)).^2 + s3(i) * (xx(j) - x(i)).^3;
end