Galperin A. Iterative methods without inversion

Boca Raton: CRC Press, 2017. — 200 p.
Iterative Methods without Inversion presents the iterative methods for solving operator equations f(x) = 0 in Banach and/or Hilbert spaces. It covers methods that do not require inversions of f (or solving linearized subproblems). The typical representatives of the class of methods discussed are Ulm’s and Broyden’s methods. Convergence analyses of the methods considered are based on Kantorovich’s majorization principle which avoids unnecessary simplifying assumptions like differentiability of the operator or solvability of the equation. These analyses are carried out under a more general assumption about degree of continuity of the operator than traditional Lipschitz continuity: regular continuity.Tools of the trade
Ulm's method
Ulm's method without derivatives
Broyden's method
Optimal secant updates of low rank
Optimal secant-type methods
Majorant generators and their convergence domains.