ABSTRACT
Let X, H, and L(H,X) be a Banach space, a Hilbert one with the inner product 〈· , ·〉, and the Banach space of linear bounded operators acting from H into X. Broyden’s method [4] (in its inversion-free form), given a starting pair (x0 ,A0) ∈ X × L(H,X), generates the sequence of iterations (xn,An) according to the following rule:
x+ := x−Af(x) , A+ := A− Af(x+)〈A∗Af(x) , f(x+)− f(x)〉 〈A ∗Af(x) , ·〉 , (4.1)
where A∗ is the adjoint of A.
