Algorithms to compute CM- and S-estimates for regression

Experiences with Cm/avs to Visualize and Compute Simulation Data on the Cm-5 (1)

We have used AVS and its parallel implementation, CM/AVS, to create a distributed environment between a Silicon Graphics IRIS Crimson workstation and a CM-5 Connection Machine parallel supercomputer from Thinking Machines Corporation. This heterogeneous distributed system is used to visualize data generated from simulations on the CM-5. CM/AVS modules have been developed to read, process, and v...

Algorithms to Compute the Lyndon Array

In the Lyndon array λ = λx[1..n] of a string x = x[1..n], λ[i] is the length of the longest Lyndon word starting at position i of x. The computation of λ has recently become of great interest, since it was shown (Bannai et al., The “Runs” Theorem [2]) that the runs in x are computable in linear time from λx. Here we first describe three algorithms for computing λx that have been suggested in th...

Eleven Simple Algorithms to Compute Fibonacci Numbers

The Fibonacci numbers are a sequence of integers in which every number after the first two, 0 and 1, is the sum of the two preceding numbers. These numbers are well known and algorithms to compute them are so easy that they are often used in introductory algorithms courses. In this paper, we present eleven of these well-known algorithms and some of their properties. These algorithms, though ver...

Signature-based algorithms to compute standard bases

Signature-based algorithms to compute Groebner bases

This paper describes a Buchberger-style algorithm to compute a Gröbner basis of a polynomial ideal, allowing for a selection strategy based on " signatures ". We explain how three recent algorithms can be viewed as different strategies for the new algorithm, and how other selection strategies can be formulated. We describe a fourth as an example. We analyze the strategies both theoretically and...