A new algebraic technique for the construction of interactive proof systems is presented. Our
technique is used to prove that every language in the polynomial-time hierarchy has an …

The emergence and continuing use of multi-core architectures and graphics processing
units require changes in the existing software and sometimes even a redesign of the …

Solving dense linear systems of equations is a fundamental problem in scientific computing.
Numerical simulations involving complex systems represented in terms of unknown …

The computation of the singular value decomposition, or SVD, has a long history with many
improvements over the years, both in its implementations and algorithmically. Here, we …

This work revisits existing algorithms for the QR factorization of rectangular matrices
composed of p× q tiles, where p≥ q. Within this framework, we study the critical paths and …

Gaussian elimination is a canonical linear algebra procedure for solving linear systems of
equations. In the last few years, the algorithm has received a lot of attention in an attempt to …

One of the major trends in the design of exascale architectures is the use of multicore nodes
enhanced with GPU accelerators. Exploiting all resources of a hybrid accelerators-based …

We present a new approach to utilizing all CPU cores and all GPUs on heterogeneous
multicore and multi-GPU systems to support dense matrix computations efficiently. The main …

This paper introduces a novel implementation in reducing a symmetric dense matrix to
tridiagonal form, which is the preprocessing step toward solving symmetric eigenvalue …

We design and develop a new high performance implementation of a fast direct LU-based
solver using low-rank approximations on massively parallel systems. The LU factorization is …