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, ...

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 ...

Matrix factorization techniques have become pivotal in data mining, enabling the extraction of latent structures from large-scale data matrices. These methods decompose complex datasets into ...