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**Subject Mathematics Numerical Analysis**

Check the file: Questions.pdf

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4.

a.

function weights = barywghts(x)

X = repmat(x(:), [1 numel(x)]);

xi = reshape(X(~eye(size(X))),size(X,1),size(X,2)-1);

xj = X(:,1:end-1);

weights = 1./prod(xj - xi, 2);

end

b.

function p = baryinterp(x,f,t)

x = x(:);

t = t(:);

f = f(:);

m = numel(t);

w = barywghts(x);

p = zeros(size(t));

for i=1:m

interpPt = t(i) == x;

if any(interpPt)

temp = f(interpPt);

p(i) = temp(1);

else

deno = sum(w./(t(i)-x),1);

nume = sum((w.*f)./(t(i)-x),1);

p(i) = nume/deno;

end

end

end...

a.

function weights = barywghts(x)

X = repmat(x(:), [1 numel(x)]);

xi = reshape(X(~eye(size(X))),size(X,1),size(X,2)-1);

xj = X(:,1:end-1);

weights = 1./prod(xj - xi, 2);

end

b.

function p = baryinterp(x,f,t)

x = x(:);

t = t(:);

f = f(:);

m = numel(t);

w = barywghts(x);

p = zeros(size(t));

for i=1:m

interpPt = t(i) == x;

if any(interpPt)

temp = f(interpPt);

p(i) = temp(1);

else

deno = sum(w./(t(i)-x),1);

nume = sum((w.*f)./(t(i)-x),1);

p(i) = nume/deno;

end

end

end...

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