An improved least squares solution technique for multi-processor architecture

An approach is suggested to map the solution of the least-square (LS) problem, using Gram-Schmidt (GS) orthogonalization, on a distributed memory parallel processing (DMPP) architecture. Using algorithmic partitioning, the resulting lower-order problems are mapped concurrently on the architecture concerned so that the computational loads are more evenly balanced than when the conventional method is applied. This results in much higher multiprocessor efficiencies. Specific implementation advantages are seen to exist for the partitioning factors which are a power of 2. DMPP architectures are very useful for future implementation of high speed digital processing (DSP) applications because of the excellent potential they offer for being able to be implemented in the form of VLSIs. The solution of the problem concerned on the ring and torus topologies is discussed