Matrix computations (3rd ed.)
Efficient management of parallelism in object-oriented numerical software libraries
Modern software tools for scientific computing
Parallel implementation of a multilevel modelling package
Computational Statistics & Data Analysis - Special issue on parallel processing and statistics
A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems
SIAM Journal on Scientific Computing
Computational Economics - Computational Studies at Stanford
An updated set of basic linear algebra subprograms (BLAS)
ACM Transactions on Mathematical Software (TOMS)
Structured automatic differentiation
Structured automatic differentiation
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Restricted maximum likelihood (REML) estimation of variance-covariance matrices is an optimization problem that has both scientific and industrial applications. Parallel REML gradient algorithms are presented and compared for linear models whose covariance matrix is large, sparse and possibly unstructured. These algorithms are implemented using publicly available toolkits and demonstrate that REML estimates of large, sparse covariance matrices can be computed efficiently on multicomputers with hundreds of processors by using an effective mixture of data distributions together with a mixture of dense and sparse linear algebra kernels.