% Script Pathos.m
% pathological matrices for GE with partial pivoting
% uses toeplitz to construct the matrices
format short e;

n = 60;
A = toeplitz([1 -ones(1,n-1)],[1 zeros(1,n-1)]);
A(:,30) = 1;

x_exact = rand(n,1);
b = A*x_exact;   % create rhs so that x_exact is exact solution
x = A\b;

relerr = (x_exact-x)./x
norm(relerr,inf)
max(abs(relerr))  % same as inf norm!