In conjugate gradient method, A is positive definite.

$\displaystyle x^{(k+1)}=\sum_{j=0}^{k}{\omega^{(j)}d^{(j)}} \ \ \omega^{(j)}>0 $

show that the sequence $\displaystyle \{ ||x^{(j)}|| : j=0,...,k+1 \} $

is monotonically increasing.

- Oct 31st 2009, 10:13 PMpengchao1024prove this sequence in conjugate gradient method is incresing
In conjugate gradient method, A is positive definite.

$\displaystyle x^{(k+1)}=\sum_{j=0}^{k}{\omega^{(j)}d^{(j)}} \ \ \omega^{(j)}>0 $

show that the sequence $\displaystyle \{ ||x^{(j)}|| : j=0,...,k+1 \} $

is monotonically increasing.