function schauder_t = evalSchauderFunction(N,t)
    
    nfun = 2^(N+1);
    
    schauder_t = zeros(nfun, size(t,2));

    schauder_t(1,:) = t;
    schauder_t(2,:) = t.*(t <= 1/2) - (t-1).*(t > 1/2);
    
    for n=1:N
        H = 2^(-(n+2)/2);
        for k=2^n:2^(n+1)-1
            a = (k - 2^n)/2^n;
            b = (k - 2^n + 0.5)/2^n;
            c = (k - 2^n + 1)/2^n;
            schauder_t(k+1,:) =   H*(t - a)/(b - a).*(t >= a).*(t < b) ...
                                + H*(t - c)/(b - c).*(t >= b).*(t < c) ;
        end
    end
    
end