Prediction Properties of Aitken's Iterated Delta^2 Process, of Wynn's Epsilon Algorithm, and of Brezinski's Iterated Theta Algorithm

The prediction properties of Aitken's iterated Delta^2 process, Wynn's epsilon algorithm, and Brezinski's iterated theta algorithm for (formal) power series are analyzed. As a first step, the defining recursive schemes of these transformations are suitably rearranged in order to permit the derivation of accuracy-through-order relationships. On the basis of these relationships, the rational approximants can be rewritten as a partial sum plus an appropriate transformation term. A Taylor expansion of such a transformation term, which is a rational function and which can be computed recursively, produces the predictions for those coefficients of the (formal) power series which were not used for the computation of the corresponding rational approximant.Comment: 34 pages, LaTe

Polynomial Time Nondimensionalisation of Ordinary Differential Equations via their Lie Point Symmetries

Lie group theory states that knowledge of a $m$-parameters solvable group of symmetries of a system of ordinary differential equations allows to reduce by $m$ the number of equation. We apply this principle by finding dilatations and translations that are Lie point symmetries of considered ordinary differential system. By rewriting original problem in an invariant coordinates set for these symmetries, one can reduce the involved number of parameters. This process is classically call nondimensionalisation in dimensional analysis. We present an algorithm based on this standpoint and show that its arithmetic complexity is polynomial in input's size

Symmetric operations for all primes and Steenrod operations in Algebraic Cobordism

In this article we construct Symmetric operations for all primes (previously known only for p=2). These unstable operations are more subtle than the Landweber-Novikov operations, and encode all p-primary divisibilities of characteristic numbers. Thus, taken together (for all primes) they plug the gap left by the Hurewitz map L ---> Z[b_1,b_2,...], providing an important structure on Algebraic Cobordism. Applications include: questions of rationality of Chow group elements - see [11], and the structure of the Graded Algebraic Cobordism. We also construct Steenrod operations of T.tom Dieck-style in Algebraic Cobordism. These unstable multiplicative operations are more canonical and subtle than Quillen-style operations, and complement the latter.Comment: 21 page