Homework 2 Spring 2014 Solutions - Math 408 Homework Set 2...

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Math 408Homework Set 2This homework set will focus on the linear least squares problemLLSminxRn12kAx-bk22,whereARm×nandbRm.(1) Listed below are two functions. In each case write the problem minxf(x) as a linear least squaresproblem by specifying the matrixAand the vectorb, and then solve the associated problem.SOLUTION METHOD:Observe thatkAx-bk22:= (A1·x-b1)2+ (A2·x-b2)2+. . .(Am·x-b1m)2,whereAi·is theith row ofA. We apply this to the first function below. A similar procedure appliesto the second.(a)f(x) = (2x1-x2+ 1)2+ (x2-x3)2+ (x3-1)2
SOLUTION METHOD:The solution technique for this problem is described on the first page of Chapter 3 in the notes (i.e.,page 21).

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