function Apr11()
% If a = diag(T) and b = diag(T,-1) and pk(x) = det(T(1:k,1:k)-xI)); then
% if p_{0}(x) = 1, p_{1}(x) = a(1)-x, then for k=2:n
%
%       p_{k}(x) = (a(k) - x)*p_{k-1}(x) - b_{k-1}^{2}p_{k-2}(x)
%
% It follows that p'_{0}(x) = 0,p'_{1} = -1; and for k=2:n
%
%  p'_{k}(x) = -p_{k-1}(x) + (a_{k}-x)*p'_{k-1}(x) - b_{k-1}^2*p'_{k-2}(x)
%
% The recursions for the p_{k} and the p'_{k} can be run at the same time
% leading to an O(n) computation that computes both p_{n}(x) and p'_{n}(x).
