fix inv warning in matlab
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I use this code:
b=inv(A'*A)*A'*y;
Matlab gives warning. never use inv to solve linear system
How can I fix it?
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Accepted Answer
Walter Roberson
on 28 Jul 2019
b=inv(A'*A)*A'*y;
Multiply both sides on the left by A'*A :
(A'*A) * b = (A'*A) * inv(A'*A) * A' * y
and for any invertable matrix, X * inv(X) is the identity matrix so (A'*A) * inv(A'*A) cancels out to identity, so
(A'*A) * b = A' * y
Multiply both sides on the left by inv(A'):
inv(A') * A' * A * b = inv(A') * A' * y
and inv(A') * A' cancels to the identity on both sides, so
A * b = y
Multiply by inv(A) on the left on both sides:
inv(A) * A * b = inv(A) * y
inverse cancels to identity, so
b = inv(A) * y
Now use the \ operator:
b = A \ y;
The above mathematics might not strictly apply if A is not a square matrix.
8 Comments
Walter Roberson
on 2 Aug 2019
Yes, I missed the HH pre-multiplier, but Yes, that logic appears correct. If you try it with actual random matrices, you will find that RR is 0 to within round-off error (e.g., for rand(15,15) all of the entries come out with absolute value less than 1E-13
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