It is well known that an invertible matrix admits a factorization as a product of a lower triangular matrix L and an upper triangular matrix U if and only if all the principal minors of the matrix are ...

Common techniques for fine-tuning the performance of automatically vectorized loops in applications for Intel® Xeon Phi™ coprocessors are discussed. These techniques include strength reduction, ...

Nonnegative Matrix Factorization (NMF) has emerged as a powerful tool in data analysis, particularly noted for its ability to produce parts‐based, interpretable representations from high-dimensional ...

A symbolic formula is given for the square-root-free Cholesky decomposition of the variance-covariance matrix of the multinomial distribution. The evaluation of the symbolic Cholesky factors requires ...