Conway hemirings are Conway semirings without a multiplicative unit. We also define iteration hemirings as Conway hemirings satisfying certain identities associated with the finite groups. Iteration hemirings are iteration semirings without a multiplicative unit. We provide an analysis of the relationship between Conway hemirings and (partial) Conway semirings and describe several free construc...

The quasi-Laguerre iteration has been successfully established, by the same authors, in the spirit of Laguerre’s iteration for solving the eigenvalues of symmetric tridiagonal matrices. The improvement in efficiency over Laguerre’s iteration is drastic. This paper supplements the theoretical background of this new iteration, including the proofs of the convergence properties.

This paper is an overview of results' on the subword complexity of various classes of languages obtained by iterating a mapping, and more precisely on the asymptotic behaviour of this complexity. In the first section we consider iterated morphisms, that is DOL languages. In this area the subword complexity falls into one of five classes, and class membership can be determined. The second sectio...

We prove that iteration theories can be introduced as algebras for the monad Rat on the category of signatures assigning to every signature Σ the rationalΣ-tree signature. This supports the result that iteration theories axiomatize precisely the equational properties of least fixed points in domain theory: Rat is the monad of free rational theories and every free rational theory has a continuou...

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...

This paper is about the study of B-FQI, an Approximated Value Iteration (AVI) algorithm that exploits a boosting procedure to estimate the action-value function in reinforcement learning problems. B-FQI is an iterative off-line algorithm that, given a dataset of transitions, builds an approximation of the optimal action-value function by summing the approximations of the Bellman residuals acros...

Compared to Krylov space methods based on orthogonal or oblique projection, the Chebyshev iteration does not require inner products and is therefore particularly suited for massively parallel computers with high communication cost. Here, six different algorithms that implement this method are presented and compared with respect to roundoff effects, in particular, the ultimately achievable accur...

Value Pursuit Iteration (VPI) is an approximate value iteration algorithm that finds a close to optimal policy for reinforcement learning problems with large state spaces. VPI has two main features: First, it is a nonparametric algorithm that finds a good sparse approximation of the optimal value function given a dictionary of features. The algorithm is almost insensitive to the number of irrel...

We present a new hybrid algorithm based on Godunov’s method for computing eigenvectors of symmetric tridiagonal matrices and Inverse Iteration, which we call the Godunov–Inverse Iteration. We use eigenvectors computed according to Godunov’s method as starting vectors in the Inverse Iteration, replacing any nonnumeric elements of Godunov’s eigenvectors with random uniform numbers. We use the rig...

Let E be an arbitrary real Banach space andK a nonempty, closed, convex (not necessarily bounded) subset of E. If T is a member of the class of Lipschitz, strongly pseudocontractive maps with Lipschitz constant L ≥ 1, then it is shown that to each Mann iteration there is a Krasnosleskij iteration which converges faster than the Mann iteration. It is also shown that the Mann iteration converges ...