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Review_questions - Review questions Math 224 Fall 2011 Dr...

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Unformatted text preview: Review questions Math 224 - Fall 2011 Dr. Mauro Maggioni Office hours : Tue 4-5, in office 293 Physics Bldg. Phone : 660-2825 Web page : www.math.duke.edu/˜ mauro E-mail : mauro.maggioni at duke.edu Some the exercises below are taken or adapted from Heath’s textbook Scientific Computing square For which of the following classes of matrices of order n can the eigenvalues be computer in a finite number of steps for arbitrary n ? • Diagonal • Tridiagonal • Triangular • Hessenberg • General real matrix with distinct eigenvalues • General real matrix with eigenvalues that are not necessarily distinct square Let x be the solution of the least squares problem Ax ≅ b , where A = 1 2 1 2 1- 1 3 1- 1 . If r = Ax- b is the corresponding residual, which of the following is a possible value of r T ? Why? [1 , 1 , 1 , 1] , [- 1 ,- 1 , 1 , 1] , [- 1 , 1 , 1 ,- 1] ....
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