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this expression of the optimal A is called the Rayleigh quotient of A in x.
^k = Vk AVk (Rayleigh quotient as in §19.2)
v = w/norm(w); % new v w = A*v; % new w mu = v'*w; % Rayleigh quotient r = w - mu*v; % residual omega = norm(r)/normA; % backward error estimate Co end 20.4 Power iteration generally converges to an eigenvector corresponding to the
yk = vkAvk (Rayleigh quotient from §19.2)
20.7 To avoid the explicit matrix multiplication Av^ during the evaluation of the Rayleigh quotients Fk = v^Av^ and residuals = Av^ - ^v^, the following auxiliary quantities are introduced:
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