Chapter 30, Problem 5P

Program Plan Intro

To prove that $A\left(x\right)\mathrm{mod}\left(x-z\right)=A\left(z\right)$ for any point z .

Program Plan Intro

To prove that $Q_{kk}\left(x\right)=A\left(x_k\right)$ and $Q_{0,n-1}\left(x\right)=A\left(x\right)$ .

Program Plan Intro

To prove that $Q_{ik}\left(x\right)=Q_{ij}\left(x\right)\mathrm{mod}{P}_{ik}\left(x\right)$ and $Q_{kj}\left(x\right)=Q_{ij}\left(x\right)\mathrm{mod}{P}_{kj}\left(x\right)$ for $i\le k\le j$ .

Program Plan Intro

To write an algorithm to evaluate $A\left(x_0\right),A\left(x_1\right),\mathrm{...},A\left(x_{n-1}\right)$ that runs in $O\left(n{\lg }^{2}n\right)$ time.