68 lines
2.6 KiB
Plaintext
68 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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[ 1.77635684e-15 -2.22044605e-15 -8.88178420e-16 8.88178420e-16
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0.00000000e+00]
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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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[ 1.77635684e-15 -2.22044605e-15 -8.88178420e-16 8.88178420e-16
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0.00000000e+00]
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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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[ 7.28306304e-14 -4.44089210e-16 -2.66453526e-14 -1.62092562e-14
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-5.28466160e-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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[-5.45297141e-12 -7.28239691e-12 -3.44613227e-13 -4.24371649e-12
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-4.86499729e-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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[1.85714297 1.00000012 3.14285716 1.28571442 3.85714302]
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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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[1.11406275e-07 1.19209290e-07 1.91642426e-08 1.35516231e-07
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1.67459071e-07]
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For ε = 1e-08:
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LinAlgError for eps=1e-08: Singular matrix
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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 1.28571428 3.85714286]
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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-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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[1.81820151 1. 3.18179849 2.29149804 2.89030045]
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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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[2. 1. 3. 2.5 2.5]
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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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