Diagonally dominant matrix gaussian elimination
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☆☆ranshsangwan☆☆
let AA be an nn by nn matrix with real entries such that ∀k∈N,k≤n∀k∈N,k≤n:
∑i≠k|Ai,k|<|Akk|∑i≠k|Ai,k|<|Akk|
Show that if we were to do gauss elimination (or LU factorization) of AA, then there will be no need for row changes, no need for partial pivoting.
I don't see why this is true, I'd appreciate a hint in the right direction. Maybe I should take a general nnby nn matrix that is diagonly dominant, try to LULUfactor it and see that I don't need row changes? is this the way
let AA be an nn by nn matrix with real entries such that ∀k∈N,k≤n∀k∈N,k≤n:
∑i≠k|Ai,k|<|Akk|∑i≠k|Ai,k|<|Akk|
Show that if we were to do gauss elimination (or LU factorization) of AA, then there will be no need for row changes, no need for partial pivoting.
I don't see why this is true, I'd appreciate a hint in the right direction. Maybe I should take a general nnby nn matrix that is diagonly dominant, try to LULUfactor it and see that I don't need row changes? is this the way
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