q118085f04

q118085f04 - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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MIT OpenCourseWare http://ocw.mit.edu 18.085 Computational Science and Engineering I Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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18.085 Quiz 1 October 4, 2004 Professor Strang Your name is: Grading 1. 2. 3. 4. OPEN BOOK EXAM Write solutions onto these pages ! Circles around short answers please !! 1) (32 pts.) This problem is about the symmetric matrix 2 1 0 H = 1 2 1 0 1 1 (a) By elimination ﬁnd the triangular L and diagonal D in H = LDL T . H (b) What is the smallest number q that could replace the corner entry 33 = 1 and still leave H positive semi deﬁnite ? q = (c) H comes from the 3-step framework for a hanging line of springs: A C A T displacements −→ elongations −→ spring forces −→ external force f What are the speciﬁc matrices A and C in H = A T CA ?
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q118085f04 - MIT OpenCourseWare http:/ocw.mit.edu 18.085...

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