Multiple Quadratic Forms: A Case Study in the Design of Scalable Algorithms

Parallel implementations of the computationally intensive task of solving multiple quadratic forms (MQFs) have been examined. Coupled and uncoupled parallel methods are investigated, where coupling relates to the degree of interaction among the processors. Also, the impact of partitioning a large MQF problem into smaller non-interacting subtasks is studied. Trade-offs among the implementations fo various data-size/machine-size ratios are categorized in terms of complex arithmetic operation counts, communicatino overhead, and memory storage requirements.