This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 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 . 18085 FALL 2002 EXAM 1 SOLUTIONS DETAILED SOLUTIONS Problem 1 Let x = (tl, ..., t,) and b = (bl, ..., b,). Then and we would like to solve (but can't) The short answer is that ATA is always positive definite. The long answer is that A is of rank 1only if all tl = ... = t, (all measurements taken at the same time and the m points lie on one vertical line). In that extreme case ATA is positive semidefinite. We have for the matrix ATA: If the center of mass is at the origin (i.e. C ti = C bi = 0) then ehen we solve the resulting system [ T c"t: ] [ ; ] = [ = : t i ] we get The fact that C = 0 indicates that the least squares line b = D t passes through the origin. For all points t o lie on the same line we must have one of the following 1. (from geometric considerations) b2  bl  b3  b2 t2  tl...
View Full
Document
 Fall '10
 staff

Click to edit the document details