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CS205A midterm1_practice2

Scientific Computing

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CS205 Sample Midterm #1 Multiple choice questions [8 × 1pt=8pts] 1. The eigenvalues of the Householder matrix I - 2 vv T v T v are . . . [circle the best answer] (a) All equal to 1 (b) 1 and 0 (c) 1 and - 1 (d) 1 and - 2 2. Consider an n × n positive definite matrix A . Which of the following statements are always true about A ? [circle all that apply] 3. We often prefer to use an iterative rather than a direct method for solving a linear system because . . . [circle all that apply] (a) They can exploit the sparsity of a matrix better than direct methods do (b) They can be used for any matrix and their computational cost is at most the same as direct methods (c) They converge very fast for specific classes of matrices, especially with preconditioning (d) Direct methods provide a single result with no potential for im- provement while with iterative methods we can keep improving our
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