AAE-NA-Labs/Direct Methods for Solving Linear Systems/Alg3_forward_substitution.m

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Matlab

% Algorithm 3: Forward Substitution (Alg. 3.1.1)
function b = Alg3_forward_substitution(L, b)
[n, m] = size(L);
if n ~= m
error('Matrix is not squared!')
end
if length(b) ~= n
error('Vector b has wrong length!')
end
b(1, :) = b(1, :)/L(1,1);
for i = 2:n
b(i, :) = (b(i, :) - L(i, 1:i-1)*b(1:i-1, :))/L(i, i);
end