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...Differentiation of the cholesky decomposition iain murray february abstract wereviewstrategies for differentiating matrix based computations and derive symbolic algorithmic update rules expressions containing we recommend new blocked algorithms on algorithm dpotrf in lapack library which uses level operations from blas so is cache friendly easy to parallelize large matrices resulting are fastest waytocomputecholesky derivatives an order magnitude faster than common usage some computing environments symbolically derived updates small those approaches can be combined get best both worlds introduction l a symmetric positive denite unique lower triangular with diagonal elements satisfying ll alternatively routines compute upper u this note compares ways differentiate function larger section consider compact results longer existing computer code that differentiates decompositions often approach proposed by smith manually applying ideas behind automatic e g baydin et al numerical experiments...