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Exercise 12 - Operation Count

A student X is interested in solving the system Anxnx = b using Crout's method. However, a friend of her, Y has already worked out the LU decomposition for the matrix PA where P is typically a non singular matrix used in biological application. Can X still use this information to solve the original system? If so, how many division, multiplication and additions would be required?

Answer:
Ax = b
PAx = Pb
LUx = Pb
Let Ux = y, then Ly = Pb
y can be found using forward substitution and x can be found using backward substitution.
So Total multiplication = 2n2 - n
Total addition = 2 (n2 - n)
Total division = 2n
Total = 4n2 - n
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