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Unformatted text preview: x * that satises the equation Ax * =-b . Show that if x (0) is chosen so that x (0)-x * is an eigenvector of A , then the steepest descent method reaches x * in one stepi.e., x (1) = x * . 4. (532 only) Let f : R n R be a function with continuous rst-order partial derivatives on R n , and let M be a subspace of R n . (a) Suppose x * M minimizes f on M . Show that f ( x * ) M . (Hint: Let x M and consider the function ( t ) = f ( x * + tx ) . ) (b) Under the assumption that f is also convex, show that any x * M such that f ( x * ) M is a global minimizer of f on M ....
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- Spring '12
- Critical Point