partial pivoting

partial pivoting

clear

clc

function x = partialpivot(A,b)

n = length(b);

Ab = [A b];

for i = 1:n-1

maxval = abs(Ab(i,i));

maxrow = i;

for k = i+1:n

if abs(Ab(k,i)) > maxval

maxval = abs(Ab(k,i));

maxrow = k;

end

end

temp = Ab(i,:);

Ab(i,:) = Ab(maxrow,:);

Ab(maxrow,:) = temp;

for j = i+1:n

m = Ab(j,i)/Ab(i,i);

Ab(j,i:n+1) = Ab(j,i:n+1) - m*Ab(i,i:n+1);

end

end

x = zeros(n,1);

x(n) = Ab(n,n+1)/Ab(n,n);

for i = n-1:-1:1

sum_ax = 0;

for j = i+1:n

sum_ax = sum_ax + Ab(i,j)*x(j);

end

x(i) = (Ab(i,n+1)-sum_ax)/Ab(i,i);

end

end