Textbook: "Numerical Optimization" by Jorge Nocedal and Stephen J. Wright, Springer, Second Edition, 2006

Consider the CG iteration (Algorithm 5.2) for minimizing a quadratic and convex function f(x) = x? Ar-61x. Let x* = A-16 be the optimal solution and ex = 12-** be the error at step k. Show that ek is orthogonal to all previous search directions, Pi. i = 0.....k - 1, with respect to the inner product (07, 02) = Av. Consider the CG iteration (Algorithm 5.2) for minimizing a quadratic and convex function f(x) = x? Ar-61x. Let x* = A-16 be the optimal solution and ex = 12-** be the error at step k. Show that ek is orthogonal to all previous search directions, Pi. i = 0.....k - 1, with respect to the inner product (07, 02) = Av