Unformatted text preview: CME302 Homework 8 (1) Given a symmetric positive definite matrix A and a vector b. Show that solving the system of linear equations: Ax = b is equivalent to solving the optimization problem: 1 min xT A x - xT b x 2 (2) (1) (2) Suppose we start with x(0) = b and at each iteration, search direction is chosen to be, p(n) = r(n) = b - Ax(n) . Then show that: x(n) Kn+1 (b, A) n (3) Problem 38.6 from T.B. (3) 1 ...
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- Fall '09
- Linear Algebra, positive definite matrix