Question: A 1,658-by-50 matrix AA has the full singular value decomposition A=UVTA=UVT where the singular values are 1=20,2=2,3=0.01,1=20,2=2,3=0.01, and i=0,i=4,5,...,50i=0,i=4,5,...,50 . Let uiui and vivi be
A 1,658-by-50 matrix AA has the full singular value decomposition A=UVTA=UVT where the singular values are 1=20,2=2,3=0.01,1=20,2=2,3=0.01, and i=0,i=4,5,...,50i=0,i=4,5,...,50 . Let uiui and vivi be the ith column of UU and VV respectively. You want a solution to AwdAwd, where d=6u22u5d=6u22u5.
Solve the least-squares problem minw||Awd||22minw||Awd||22 using the rank-2 truncated singular value regularization. Denote the solution by wtr-SVDwtr-SVD.
a) (4 pts) Find wtr-SVDwtr-SVD in terms of singular vectors and values, and simplify your answer as much as possible.
b) (2 pts) Compute the squared error,||Awtr-SVDd||22||Awtr-SVDd||22. Your answer should be numerical.
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