Solving linear systems, often accomplished by iterative algorithms, is a ubiquitous task in science and engineering. To accommodate the dynamic range and precision requirements, these iterative ...

$$\begin{aligned} \frac{1}{2}&\Vert x-\mathscr {G}x\Vert \le \Vert x-y\Vert \implies \\&\Vert \mathscr {G}x-\mathscr {G}y\Vert \le \alpha \Vert x-\mathscr {G}y\Vert ...

Newton's method is actually a special case of what is generally known as a fixed point method. These methods rely on the Fixed point Theorem: ...