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Unformatted text preview: CS205 Midterm 1 Multiple-answer multiple-choice questions [7pts] 1. Which of the following statements about the solution to the linear least- squares problem are true? (a) It satisfies Ax = b . r 6 = , in general. (b) It can be found by solving the linear system A T Ax = A T x . It can be found by solving the linear system A T Ax = A T b . (c) It cannot be computed by the normal equations. The normal equations give the solution. (d) F Its associated residual lies in the nullspace of A T . This is a consequence the least-squares solution corresponding to an orthogonal projection. (e) F It can be computed by performing a QR decomposition via Householder transformations. This is, in fact, the preferred method. 2. For which of the following reasons do iterative methods typically use the residual to measure convergence? (a) F Absolute error is difficult to compute directly. In fact, it is often impossible to do so. (b) Relative error does not indicate how close a given iterate is to the exact solution. This is directly contradictory to the definition of relative error. (c) F The residual will be zero if the current iterate is a solution. This follows from the definition of residual. (d) Using the residual is equivalent to using the absolute error. The residual and the absolute error are completely different entities. 1 3. Which of the following statements about condition numbers are true? (a) The choice of b affects the condition number of Ax = b . The ratio that defines the condition number of this problem in no way depends on b ....
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This homework help was uploaded on 01/29/2008 for the course CS 205A taught by Professor Fedkiw during the Fall '07 term at Stanford.
- Fall '07