Let $A$ be a positive definite matrix. Consider the function $\phi(x)=\frac12 \langle Ax,x\rangle−\langle b,x\rangle$ and the iteration $x+\delta_iv_i\to x$ where $v_i$ is the $i$-th eigenvector of $A$ (normalized).
I don't understand what is the function $\phi(x)=\frac12\langle Ax,x\rangle−\langle b,x\rangle $? Does it refer to fixed point iteration such that $x+\delta_iv_i=\phi(x)=\frac12\langle Ax,x\rangle−\langle b,x\rangle $?
Thanks in advance.