CS205A midterm1_practice1

Scientific Computing

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CS205 Practice Midterm #1 Multiple choice questions [7pts] 1. What can you say about a least squares solution? (a) It satisfies Ax = b (b) It is given by the solution to the linear system A T Ax = A T x (c) It cannot be computed by the normal equations. (d) The corresponding residual lies in the nullspace of A T (e) It can be solved by performing a QR transformation with House- holder. 2. For which of the following reasons do iterative methods typically use the residual to measure convergence? [1pt, circle all that apply] (a) Absolute error is difficult to compute directly. (b) Relative error does not indicate closeness to the solution. (c) The residual will be zero if the current iterate is a solution. (d) Using the residual is equivalent to using the absolute error. 3. Which of the following are true about condition numbers? (a) The choice of b affects the condition number of Ax = b (b) A problem is poorly conditioned if its condition number is near zero (c) If the condition number is negative the determinant of the matrix is also negative.
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