70 lines
2.6 KiB
Plaintext
70 lines
2.6 KiB
Plaintext
Question 1(a):
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Projection of b onto the column space of A(1): (Using proj function)
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Projection of b onto the column space of A(1): (Using proj_SVD function)
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Difference between the two methods:
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[ 2.22044605e-16 1.55431223e-15 -4.44089210e-16 2.22044605e-16
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-8.88178420e-16]
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Question 1(b):
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For ε = 1.0:
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Projection of b onto the column space of A(1.0):
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Projection of b onto the column space of A(1.0) using SVD:
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Difference between the two methods:
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[ 2.22044605e-16 1.55431223e-15 -4.44089210e-16 2.22044605e-16
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-8.88178420e-16]
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For ε = 0.1:
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Projection of b onto the column space of A(0.1):
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Projection of b onto the column space of A(0.1) using SVD:
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Difference between the two methods:
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[ 8.08242362e-14 5.87307980e-14 -8.88178420e-16 4.81836793e-14
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-1.37667655e-14]
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For ε = 0.01:
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Projection of b onto the column space of A(0.01):
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Projection of b onto the column space of A(0.01) using SVD:
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Difference between the two methods:
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[-4.76907402e-12 -1.84297022e-14 5.53779245e-13 -4.00324218e-12
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1.49613655e-12]
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For ε = 0.0001:
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Projection of b onto the column space of A(0.0001):
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[1.85714282 1. 3.14285716 1.28571427 3.85714291]
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Projection of b onto the column space of A(0.0001) using SVD:
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[1.85714286 1. 3.14285714 1.28571429 3.85714286]
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Difference between the two methods:
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[-3.59740875e-08 9.10937992e-13 1.94238092e-08 -1.19938544e-08
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4.79721098e-08]
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For ε = 1e-08:
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Projection of b onto the column space of A(1e-08):
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[-1.87500007 0.99999993 -3.12499997 -2.62500007 3.49999996]
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Projection of b onto the column space of A(1e-08) using SVD:
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[1.85714286 1. 3.14285714 1.28571427 3.85714286]
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Difference between the two methods:
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[-3.73214294e+00 -7.45058057e-08 -6.26785711e+00 -3.91071435e+00
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-3.57142909e-01]
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For ε = 1e-16:
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ValueError for eps=1e-16: Matrix A must be full rank.
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Projection of b onto the column space of A(1e-16) using SVD:
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[3.4 1. 1.6 1.8 1.8]
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Difference between the two methods:
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Could not compute difference due to previous error.
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For ε = 1e-32:
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ValueError for eps=1e-32: Matrix A must be full rank.
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Projection of b onto the column space of A(1e-32) using SVD:
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[3.4 1. 1.6 1.8 1.8]
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Difference between the two methods:
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Could not compute difference due to previous error.
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