Fall2011-HW6

Fall2011-HW6 - Let A be the n × n matrix of the form 2-1-1...

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Homework 6 Math 371, Fall 2011 Assigned: Thursday, October 20, 2011 Due: Thursday, October 26, 2011 Clearly label all plots using title , xlabel , ylabel , legend Use the subplot command to compare multiple plots Include printouts of all Matlab code, labeled with your name, date, section, etc. (1) (Norms) (a) Do problems #3(a), (b) from page 180 (b) Consider the matrix A = 2 0 0 0 3 4 0 2 - 1 . Compute the spectrum of A T A . What is the 2 matrix norm of A ? (c) Compute the matrix norm of A . Find a vector x such that A = Ax / x . (d) Verify your calculations in (b) and (c) using Matlab. (2) (Condition numbers)
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Unformatted text preview: Let A be the n × n matrix of the form 2-1-1 2-1-1 2 . . . . . . . . .-1-1 2 . Read the help of the Matlab command diag() and use it create such a matrix for any given n . (a) For n = 50 , 100 , 500 , 1000 , 2000 , 4000, ﬁnd the condition number of the matrix using cond(A) and make a table. (b) Plot the condition numbers against n using loglog() . Include your plot. (c) How do the condition numbers depend upon n ? 1...
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