Ordinary linear model estimation on a massively parallel simd computer

Abstract

Efficient algorithms for estimating the coefficient parameters of the ordinary linear model on a massively parallel SIMD computer are presented. The numerical stability of the algorithms is ensured by using orthogonal transformations in the form of Householder reflections and Givens plane rotations to compute the complete orthogonal decomposition of the coefficient matrix. Algorithms for reconstructing the orthogonal matrices involved in the decompositions are also designed, implemented and analyzed. The implementation of all algorithms on the targeted SIMD array processor is considered in detail. Timing models for predicting the execution time of the implementations are derived using regression modelling methods. The timing models also provide an insight into how the algorithms interact with the parallel computer. The predetermined factors used in the regression fits are derived from the number of memory layers involved in the factorization process of the matrices. Experimental results show the high accuracy and predictive power of the timing models.