a3

BandQR.m

function [Q,R]=BandQR(A, p)
    [n,n]=size(A);
    R=A; %Start with R=A
    Q=eye(n); %Set Q as the identity matrix
   
    
    for k=1:n-1

        x = zeros(p+1,1);
        j=min(n, k+p-1);
        
        x = R(k:j, k);
        x(1)=x(1)+norm(x);
        w=x/norm(x);
        
        u=2*R(k:j, 1:end)'*w;
        R(k:j, 1:end)=R(k:j, 1:end)-w*u';
        
        wwt = zeros(n,n);
        wwt(k:j, k:j) = w * w';
        Q=Q-2*Q*wwt;
  
    end
end