Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

We start with a discussion of coupled algebraic Riccati equations arising in the study of linear-quadratic optimal control problem for Markov jump linear systems. Under suitable assumptions, this system of equations has a unique positive semidefinite solution, which is the solution of practical interest. The coupled equations can be rewritten as a single linearly perturbed matrix Riccati equati...

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...

Some of the most successful recent applications of reinforcement learning have used neural networks and the TD( ) algorithm to learn evaluation functions. In this paper, we examine the intuition that TD( ) operates by approximating asynchronous value iteration. We note that on the important subclass of acyclic tasks, value iteration is ine cient compared with another graph algorithm, DAG-SP, wh...

We show how two iterated products of selection functions can both be used in conjunction with system T to interpret, via the dialectica interpretation and modified realizability, full classical analysis. We also show that one iterated product is equivalent over system T to Spector’s bar recursion, whereas the other is T-equivalent to modified bar recursion. Modified bar recursion itself is show...

In this paper, the Sawada-Kotera equation is solved by using the Adomian’s decomposition method, modified Adomian’s decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its comp...

Problem 1 (Convergence of Richardson iteration). This method’s operator has the form T = I − BA = I − ωA because B = ωI. The eigenvectors of T are – as is easy to verify, the same as those of A, and the eigenvalues of T are λi(T ) = 1− ωλi(A). To prove that the method converges, it is convenient to verify that the l2 norm of T is less than one because we can then express everything in terms of ...