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: ...

Let K be a compact convex subset of a real Hilbert space, H; T: K → K a continuous pseudocontractive map. Let {an}, {bn}, {cn}, {an ′}, {bn ′} and {cn ′} be real sequences in [0,1] satisfying ...

Let K be a nonempty closed convex subset of a real Banach space E and T be a Lipschitz pseudocontractive self-map of K with $F(T)\coloneq ${x∈ K: Tx=x}$\neq ...

An unfortunate reality of trying to represent continuous real numbers in a fixed space (e.g. with a limited number of bits) is that this comes with an inevitable loss of both precision and accuracy.