# prove this sequence in conjugate gradient method is incresing

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• Oct 31st 2009, 10:13 PM
pengchao1024
prove this sequence in conjugate gradient method is incresing
In conjugate gradient method, A is positive definite.
$x^{(k+1)}=\sum_{j=0}^{k}{\omega^{(j)}d^{(j)}} \ \ \omega^{(j)}>0$
show that the sequence $\{ ||x^{(j)}|| : j=0,...,k+1 \}$
is monotonically increasing.