Fall2011-HW7

Fall2011-HW7 - Homework 7 Math 371, Fall 2011 Assigned:...

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Homework 7 Math 371, Fall 2011 Assigned: Saturday, October 28, 2011 Due: Thursday, November 3, 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, and section. Add 12 for page numbers in the international edition. (1) (Condition numbers) For two n × n matrices A and B , prove that ( AB ) - 1 = B - 1 A - 1 , and ( αA ) - 1 = 1 α A - 1 . Now do P. 187 #1, 2. (2) (Residual errors vs. forward errors) As in the previous homework, let A be the n × n matrix of the form 2 - 1 - 1 2 - 1 - 1 2 . . . . . . . . . - 1 - 1 2 . Write a matlab function named [rerr, ferr, condnum] = ResidualFwdErrors(n) which takes n as an argument, generates the matrix A as above, and then a vector x , and then a vector b = Ax , and returns the relative residual error, relative forward error, and the condition number.

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Fall2011-HW7 - Homework 7 Math 371, Fall 2011 Assigned:...

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