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 August 11th, 2012, 03:52 PM #1 Newbie   Joined: Jul 2012 Posts: 6 Thanks: 0 Best least-squares approximation Given the subspace =\begin{bmatrix} x_1\\x_2\\x_3\end{bmatrix}, x_1-2x_2+x_3=0\}" /> and the vector Find a basis for the indicated subspace W. For the given vector v, solve the normal equations and determine the best approximation w*. Verify that v-w* is orthogonal to the basis vectors. I know how to find the basis and check orthogonality, and I know how to solve for w* using an orthogonal basis and how to get an orthogonal basis, but I don't understand how the normal equation is used to solve for w*. According to my textbook the normal equation is . If I understand it correctly, Ax=w* and b = v so it should be I get the feeling I'm missing something obvious and I'm using the wrong equation because can't be constructed without more information can it? August 12th, 2012, 02:26 PM #2 Newbie   Joined: Jul 2012 Posts: 6 Thanks: 0 Re: Best least-squares approximation I figured out what I was supposed to do. It took me forever to think to use the subspace as a constraint for the system of equations to solve for w*. Tags approximation, leastsquares Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Shamieh Calculus 1 October 9th, 2013 10:09 AM Alonso_Canada Algebra 28 October 23rd, 2012 09:51 AM aaron-math Calculus 1 October 3rd, 2011 12:34 PM Wissam Number Theory 16 March 13th, 2011 04:41 PM Marcel777 Number Theory 5 September 27th, 2010 11:49 PM

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