Machine iteration for a linear function

Continuous Turing Machine: Real Function Computability and Iteration Issues

Contemporary computer theory is governed by the discretization of continuous problems. Classical Turing machines (TMs) are originally built to solve computation and computability problems, which main feature is discreteness. However, even some simple numerical calculations problems, e.g., iterations in Rn, generate difficulties to be described or solved by constructing a TM. This paper explores...

Convergent Fitted Value Iteration with Linear Function Approximation

Fitted value iteration (FVI) with ordinary least squares regression is known to diverge. We present a new method, “Expansion-Constrained Ordinary Least Squares” (ECOLS), that produces a linear approximation but also guarantees convergence when used with FVI. To ensure convergence, we constrain the least squares regression operator to be a non-expansion in the∞-norm. We show that the space of fu...

Minimality in a Linear Calculus with Iteration

System L is a linear version of Gödel’s System T , where the λ-calculus is replaced with a linear calculus; or alternatively a linear λ-calculus enriched with some constructs including an iterator. There is thus at the same time in this system a lot of freedom in reduction and a lot of information about resources, which makes it an ideal framework to start a fresh attempt at studying reduction ...

A Jacobi-Davidson Iteration Method for Linear Eigenvalue Problems

In this paper we propose a new method for the iterative computation of a few of the extremal eigenvalues of a symmetric matrix and their associated eigenvectors. The method is based on an old and almost unknown method of Jacobi. Jacobi’s approach, combined with Davidson’s method, leads to a new method that has improved convergence properties and that may be used for general matrices. We also pr...

Iteration and Function Approximation