The classical Newton iteration method for matrices can be modified into an efficient algorithm when structured matrices are involved. The difficulty, however, is the importance of the choice of the starting matrix. In this paper, we propose a new initial iteration step which makes the choice of the starting matrix less critical. The validity of the approach is illustrated by numerical experiments.

Several variants of the Halpern-Läuchli Theorem for trees of uncountable height are investigated. For κ weakly compact, we prove that the various statements are all equivalent, and hence, the strong tree version holds for one tree on any weakly compact cardinal. For any finite d ≥ 2, we prove the consistency of the Halpern-Läuchli Theorem on d many normal κ-trees at a measurable cardinal κ, giv...

Sergio Ruiz-Halpern*, Raquel Vaquer-Sunyer and Carlos M. Duarte 1 Centre for Coastal Biogeochemistry, School of Environment, Science and Engineering, Southern Cross University, Lismore, NSW, Australia 2 Department of Global Change, Institut Mediterrani d’Estudis Avançats, Consejo Superior de Investigaciones Científicas, Universitat de les Illes Balears, Esporles, Spain 3 Interdisciplinary Ecolo...

Markov Decision Processes (MDPs) are used to model both non-deterministic and probabilistic systems. Probabilistic model checking is an approach for verifying quantitative properties of probabilistic systems that are modeled by MDPs. Value and Policy Iteration and modified version of them are well-known approaches for computing a wide range of probabilistic properties. This paper tries to impro...

Let E be a real Banach Space and K a nonempty closed convex (not necessarily bounded) subset of E. Iterative methods for the approximation of fixed points of asymptotically demicontractive mappings T : K → K are constructed using the more general modified Mann and Ishikawa iteration methods with errors. Our results show that a recent result of Osilike [3] (which is itself a generalization of a ...

Introduction This paper presents a work in progress on enhanced Propositional Dynamic Logics for reasoning about ac tions Propositional Dynamic Logics PDL s are modal logics for describing and reasoning about system dynamics in terms of properties of states and actions modeled as relations between states see Kozen Tiuryn Harel Parikh for surveys on PDL s see also Stirling for a somewhat di eren...

First, Halpern-type proximal point algorithm is introduced in complete CAT(0) metric spaces. Then, Browder convergence theorem is considered for this algorithm and also we prove that Halpern-type proximal point algorithm converges strongly to a zero of the operator.

In this paper we propose a novel algorithm, factored value iteration (FVI), for the approximate solution of factored Markov decision processes (fMDPs). The traditional approximate value iteration algorithm is modified in two ways. For one, the least-squares projection operator is modified so that it does not increase max-norm, and thus preserves convergence. The other modification is that we un...

The input motion for seismic analysis of building structures is generally specified in design codes in terms of response spectrum. Therefore, real or simulated time histories for ground motions whose response spectrum matches approximately the design spectrum is desired. Among the various techniques currently available for generating spectrum compatible time histories it is possible to distingu...

We present a stochastic planner based on Markov Decision Processes (MDPs) that participates to the probabilistic planning track of the 2006 International Planning Competition. The planner transforms the PPDDL problems into factored MDPs that are then solved with a structured modified value iteration algorithm based on the safest stochastic path computation from the initial states to the goal st...