We keep the notations from the previous parts. In particular, we still denote by $x _ { k }$ the minimizer of $J$ on $x _ { 0 } + H _ { k }$.
Assume that a family $\left( p _ { 0 } , \ldots , p _ { m - 1 } \right)$ of vectors satisfying the properties of question 24 is known. Show that $x _ { k + 1 } - x _ { k }$ is then collinear with $p _ { k }$ for all integer $k \in \{ 0 , \ldots , m - 1 \}$.