2016/02/24 by Iain Murray, Murray, Iain · 2 citations
Computer Science · #Computation (stat.CO) #FOS: Computer and information sciences #Graph Theory and Algorithms #Mathematical Software (cs.MS) #Matrix Theory and Algorithms #Parallel Computing and Optimization Techniques
paper · pdf · doi:10.48550/arxiv.1602.07527
openalex publication_date 2016/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review strategies for differentiating matrix-based computations, and derive symbolic and algorithmic update rules for differentiating expressions containing the Cholesky decomposition. We recommend new `blocked' algorithms, based on differentiating the Cholesky algorithm DPOTRF in the LAPACK library, which uses `Level 3' matrix-matrix operations from BLAS, and so is cache-friendly and easy to parallelize. For large matrices, the resulting algorithms are the fastest way to compute Cholesky derivatives, and are an order of magnitude faster than the algorithms in common usage. In some computing environments, symbolically-derived updates are faster for small matrices than those based on differentiating Cholesky algorithms. The symbolic and algorithmic approaches can be combined to get the best of both worlds.