cs205a

# cs205a - CS 205a Fall 2011 Midterm 2 Please write your name...

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CS 205a Fall 2011 Midterm 2 Please write your name and netid on the top right of the first page. The exam is closed book and no calculators are allowed. You have 1 hour and 15 minutes to complete the exam. Multiple Choice (4 x 1 pt each) For each of the following questions, circle ALL answers that are correct. 1. Let A be a symmetric positive definite n × n matrix that you attempt to solve using the Conjugate Gradient method. If A has 3 distinct eigenvalues, what is the maximum number of steps (in theory) that the CG solver needs to converge? (a) n (b) 3 (c) n - 3 (d) None of the above is correct. 2. Recall the Newmark method: x n +1 = x n + Δ tv n + Δ t 2 2 (1 - 2 β ) α n + 2 βα n +1 v n +1 = v n + Δ t (1 - γ ) α n + γα n +1 Which of the following methods is not equivalent for some choice of α and β parameters? (a) Constant Acceleration (b) 3 rd -order accurate Runge-Kutta. (c) Central Differencing (d) Trapezoidal Rule 3. In general, which of the following methods are the most suitable for solving heat equations?

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