eckiller
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Hello,
I have to do a proof and am having trouble starting.
The proof is to show how you could use Cholesky decomposition to determine a set of A-orthogonal directions.
Cholesky decom. means I can write the symmetric positive definite matrix as
A = GG'
The textbook gives a way of determining the A-orthogonal set using A. Specifically,
v_k = r_k-1 + s_k-1*v_k-1
where v_k is the kth direction vector and r_k-1 is the k-1 residual vector. So we want to choose s_k-1 such that
<v_k-1, Av_k> = 0
The textbook then goes onto show:
s_k-1 = - <v_k-1, Ar_k-1> / <v_k-1, Av_k-1>
So I don't see how using A = GG' helps at all.
If anyone could give me a tip on how to start, I'd be thankful.
I have to do a proof and am having trouble starting.
The proof is to show how you could use Cholesky decomposition to determine a set of A-orthogonal directions.
Cholesky decom. means I can write the symmetric positive definite matrix as
A = GG'
The textbook gives a way of determining the A-orthogonal set using A. Specifically,
v_k = r_k-1 + s_k-1*v_k-1
where v_k is the kth direction vector and r_k-1 is the k-1 residual vector. So we want to choose s_k-1 such that
<v_k-1, Av_k> = 0
The textbook then goes onto show:
s_k-1 = - <v_k-1, Ar_k-1> / <v_k-1, Av_k-1>
So I don't see how using A = GG' helps at all.
If anyone could give me a tip on how to start, I'd be thankful.