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We investigate a parallelization strategy for dense matrix factorization(DMF) algorithms, using OpenMP, that departs from the legacy (or conventional)solution, which simply extracts concurrency from a multithreaded version ofBLAS. This approach is also different from the more sophisticatedruntime-assisted implementations, which decompose the operation into tasks andidentify dependencies via directives and runtime support. Instead, our strategyattains high performance by explicitly embedding a static look-ahead techniqueinto the DMF code, in order to overcome the performance bottleneck of the panelfactorization, and realizing the trailing update via a cache-awaremulti-threaded implementation of the BLAS. Although the parallel algorithms arespecified with a highlevel of abstraction, the actual implementation can beeasily derived from them, paving the road to deriving a high performanceimplementation of a considerable fraction of LAPACK functionality on anymulticore platform with an OpenMP-like runtime.

Programming Parallel Dense Matrix Factorizations with Look-Ahead and OpenMP