CS205A midterm2_practice2

# Scientific Computing

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CS205 Mathematical Methods for Computer Vision, Robotics, and Graphics Autumn 2006 Midterm #2 The following is a statement of the Stanford University Honor Code: 1. The honor Code is an undertaking of the students, individually and collectively: (a) that they will not give or receive aid in examinations; that they will not give or receive unpermitted aid in class work, in the preparation of reports, or in any other work that is to be used by the instructor as the basis of grading; (b) that they will do their share and take an active part in seeing to it that others as well as themselves uphold the spirit and letter of the Honor Code. 2. The faculty on its part manifests its confidence in the honor of its students by refraining from proctoring examinations and from taking unusual and unreasonable precautions to prevent the forms of dishonesty mentioned above. The faculty will also avoid, as far as practicable, academic procedures that create temptations to violate the Honor Code. 3. While the faculty alone has the right and obligation to set academic requirements, the students and faculty will work together to establish optimal conditions for honorable academic work. By writing my name below, I certify that I acknowledge and accept the Honor Code. Name Stanford ID SUNet Username 1

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Multiple choice questions [4pts total, 1pt each] 1. Which of the following statements regarding numerical solution of ODEs are true? [circle all that apply] (a) Solving the linear ODE y = λy, λ < 0 using Forward Euler and a very large timestep results in an instability There is a specific maximum timestep allowed for stability (b) Solving the linear ODE y = λy, λ < 0 using Forward Euler and a very large timestep results in the solution converging to zero very rapidly The method will be unstable (c) Solving the linear ODE y = λy, λ < 0 using Backward Euler and a very large timestep results in an oscillatory behavior The solution is rapidly damped towards zero (d) Solving the linear ODE y = λy, λ < 0 using Trapezoidal Rule and a very large timestep results in an oscillatory behavior This is characteristic of trapezoidal rule as Δ t → ∞ 2. Which of the following statements regarding interpolation methods are true? [circle all that apply] (a) Newton interpolation is more convenient than interpolation using a monomial basis if the set of interpolation points needs to be incrementally updated The Newton basis is incrementally constructed and easily updated with the intro-
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