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EricDarve / numerical_linear_algebra

Julia code for the book Numerical Linear Algebra
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Typo page 286 #189

Closed noa-codes closed 4 years ago

noa-codes commented 4 years ago

In the first paragraph, in the description of Gram-Schmidt, it says

"...to find some vector \nu^{(2)} that is A-conjugate to \nu^{(2)}, and so on."

I think this should be

"...to find some vector \nu^{(2)} that is A-conjugate to \nu^{(1)}, and so on."

Since \nu^{(2)} is not orthogonal to itself.

EricDarve commented 4 years ago

That whole section has plenty of errors. Sorry. This is a recent change and the indices are wrong. Let me know if the new text makes more sense.

noa-codes commented 4 years ago

The new text does make more sense -- I am a bit confused about why we use k+1 linearly independent vector (nu_0 through nu_k) to create k A-orthogonal vectors (p_1 through p_k). Isn't Gram-Schmidt one-to-one?

EricDarve commented 4 years ago

It goes up to p^{(k+1)}. So you have k+1 vectors on both sides.

EricDarve commented 4 years ago

I made various updates to indices in that section. There were some errors with mu_k and p_k.