midterm_F19.pdf - Numerical Analysis Practice Midterm Exam...

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Numerical Analysis: Practice Midterm Exam Fall 2020 Name: This exam is scheduled for 70 minutes. It is closed book and closed notes. No calculator should be necessary. By signing your name, you agree to the NYU honor code. The exam is worth 44 points. 1
MATH-UA:Numerical Analysis (This page intentionally left blank. You can use it for scratch work.)
MATH-UA:Numerical Analysis 1 Short answer and true/false [10pts] Answer the following statements with true or false (no justification necessary), or provide a short answer for non true/false questions. 1 Newtons method can not converge with order higher than 2 2 A Householder matrix has exactly 2 unique eigen- values 3 True or false: Fixed point iteration applied to g ( x ) = 3 x 2 - 1 2 x will converge to 1 4 Householder transformation matrices H v describe re- flections on the hyperplane that is orthogonal to the vector v . 5 In terms of FLOPS, it is faster to compute a QR decom- position than an LU. 6 Given a unit vector v and some non-zero vector x what is the flop count for computing H v x ? 7 With x 0 = 1 as a starting point, Newtons method ap- plied to f ( x ) = x 1 / 3 will converge.
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