CS205A midterm2 fall07

Scientific Computing

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CS 205A Fall 2007 Midterm (8 points) Multiple Choice [circle the best answer] 1. When solving Ax = b , which of the following are true? (a) If the condition number is bad, Steepest Descent performs well. (b) When A is sparse, large and positive definite, Cholesky Factorization is the most space-efficient solver. (c) If A is negative semi-definite, we can solve this system using a modified form of Conjugate Gra- dients. (d) An incomplete cholesky preconditioner is useful when all of the eigenvalues of A are similar in magnitude. 2. When solving the characteristic ODE y 0 = λy , (a) The problem is ill-posed if λ > 0. (b) When discretized using forward euler, the method is unstable when - 2 < hλ < 0. (c) When discretized using backward euler, the method is unstable when h = λ . (d) The Trapezoidal rule is 3 rd order accurate. 3. When solving the ODE y 0 = y , which of the following methods will converge to the correct solution? (a) Forward Euler. (b) Backward Euler. (c) Trapezoidal Rule. (d) none of the above. 4. When solving Ax = b using the Conjugate Gradients algorithm, which of the following is true? (a) The search directions are orthogonal, (
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This note was uploaded on 01/29/2008 for the course CS 205A taught by Professor Fedkiw during the Fall '07 term at Stanford.

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CS205A midterm2 fall07 - CS 205A Fall 2007 Midterm (8...

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