A. Mikhalev

TL;DR: A new and flexible tile row rank Cholesky factorization is designed and a high performance implementation using OpenMP task-based programming model on various leading-edge manycore architectures is proposed, representing an important milestone in enabling large-scale simulations for covariance-based scientific applications.

TL;DR: A definition of the volume of a general rectangular matrix, which is equivalent to an absolute value of the determinant for square matrices, is introduced and three promising applications of such submatrices are presented.

TL;DR: A novel solution to the problem of solving large-scale linear systems that performs a Cholesky factorization on a symmetric positive-definite covariance matrix, which leverages fine-grained computations to facilitate asynchronous execution while providing a flexible data distribution to mitigate load imbalance.

TL;DR: The Hierarchical matrix Computations on Manycore Architectures (HiCMA) library is extended to provide a high-performance implementation on distributed-memory systems of one of the most widely used matrix factorization in large-scale scientific applications, i.e., the Cholesky factorization.

TL;DR: This tool-assisted performance analysis results in a new hybrid data distribution, a new hierarchical TLR Cholesky algorithm, and a new performance model for tuning the tile size, which achieves an 8X performance speedup over existing implementations on massively parallel supercomputers, toward solving large-scale 3D climate and weather prediction applications.