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CS205A midterm1_practice1_solutions

Scientific Computing

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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 = 0 , 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) Its associated residual lies in the nullspace of A T . This is a consequence the least-squares solution corresponding to an orthogonal projection. (e) 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) 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) 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
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CS205A midterm1_practice1_solutions - CS205 Midterm 1...

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