Median as a weighted arithmetic mean of all sample observations

This paper shows how median may be computed as a weighted arithmetic mean of all sample observations, unlike the conventional method that obtains median as the middle value (odd observations) or a simple mean of the two middlemost values (even observations). Monte Carlo experiments have been carried out to investigate the bias, efficiency and consistency of the alternative methods.

Parallel tridiagonal equation solvers

Three parallel algorithms were compared for the direct solution of tridiagonal linear systems of equations. The algorithms are suitable for computers such as ILLIAC 4 and CDC STAR. For array computers similar to ILLIAC 4, cyclic odd-even reduction has the least operation count for highly structured sets of equations, and recursive doubling has the least count for relatively unstructured sets of equations. Since the difference in operation counts for these two algorithms is not substantial, their relative running times may be more related to overhead operations, which are not measured in this paper. The third algorithm, based on Buneman's Poisson solver, has more arithmetic operations than the others, and appears to be the least favorable. For pipeline computers similar to CDC STAR, cyclic odd-even reduction appears to be the most preferable algorithm for all cases

Discretisation for odd quadratic twists

The discretisation problem for even quadratic twists is almost understood, with the main question now being how the arithmetic Delaunay heuristic interacts with the analytic random matrix theory prediction. The situation for odd quadratic twists is much more mysterious, as the height of a point enters the picture, which does not necessarily take integral values (as does the order of the Shafarevich-Tate group). We discuss a couple of models and present data on this question.Comment: To appear in the Proceedings of the INI Workshop on Random Matrix Theory and Elliptic Curve

О структуре графа разложений образующих однородных натуральных арифметических графов

The paper is finished investigated of the homogenous natural arithmetic graphs using the generatrixes separation graph. A number of the assertions were proved. Structure of the ones graphs were described and investigated both for even and odd cases