We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach...

Implicit methods for Hamilton Jacobi Bellman (HJB) partial differential equations give rise to highly nonlinear discretized algebraic equations. The classic policy iteration approach may not be efficient in many circumstances. In this article, we derive sufficient conditions to ensure convergence of a combined fixed point-policy iteration scheme for solution of the discretized equations. Numeri...

In recent years, implicit stochastic Runge–Kutta (SRK) methods have been developed both for strong and weak approximations. For these methods, the stage values are only given implicitly. However, in practice these implicit equations are solved by iterative schemes such as simple iteration, modified Newton iteration or full Newton iteration. We employ a unifying approach for the construction of ...

We analyze a number of techniques for pricing American options under a regime 4 switching stochastic process. The techniques analyzed include both explicit and implicit discretiza5 tions with the focus being on methods which are unconditionally stable. In the case of implicit 6 methods we also compare a number of iterative procedures for solving the associated nonlinear al7 gebraic equations. N...

We analyze a number of techniques for pricing American options under a regime switching stochastic process. The techniques analyzed include both explicit and implicit discretizations with the focus being on methods which are unconditionally stable. In the case of implicit methods we also compare a number of iterative procedures for solving the associated nonlinear algebraic equations. Numerical...

preprint numerics no. 4/2007 norwegian university of science and technology trondheim, norway Abstract. In the last years, implicit SRK methods have been developed both for strong and weak approximation. For these methods, the stage values are only given implicitly. However, in practice these implicit equations are solved by iterative schemes like simple iteration, modified Newton iteration or ...