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 ...

Perold, André. "A Degeneracy Exploiting LU Factorization for the Simplex Method." In Large Scale Linear Programming, edited by G. B. Dantzig, M. A. H. Dempster, and Markku Kallio. Laxenburg, Austria: ...

Complex symmetric matrices whose real and imaginary parts are positive definite are shown to have a growth factor bounded by 2 for LU factorization. This result adds to the classes of matrix for which ...

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, ...