Solving dense linear systems on platforms with multiple hardware accelerators

Solving Large Dense Systems of Linear Equations on Systems with Virtual Memory and with Cache

The problem of solving large full sets of linear equations on a computer with hierarchical memory is considered. Blocked Gaussian elimination and QR factorization are studied in an attempt to apply exactly the same implementations on computers with virtual memory as on computers with cache. This differs slightly from the LAPACK[1] approach which, although aimed at the same architectures, focuse...

Scalable Dense Linear Algebra on Heterogeneous Hardware

Design of systems exceeding 1 Pflop/s and the push toward 1 Eflop/s, forced a dramatic shift in hardware design. Various physical and engineering constraints resulted in introduction of massive parallelism and functional hybridization with the use of accelerator units. This paradigm change brings about a serious challenge for application developers, as the management of multicore proliferation ...

Certified Dense Linear System Solving

Mixed accelerated techniques for solving dense linear systems

The rounding-error analysis of Gaussian elimination shows that the method is stable only when the elements of the matrix do not grow excessively in the course of the reduction. Usually such growth is prevented by interchanging rows and columns of the matrix so that the pivot element is acceptably large. In this paper firstly we introduce the Boosting LU factorization method based on a rank one ...

Exponential Stability of Linear Systems with Multiple Time Delays

In this paper, a class of linear systems with multiple time delays is studied. The problem of exponential stability of time-delay systems has been investigated by using Lyapunov functional method. We will convert the system of multiple time delays into a single time delay system and show that if the old system is stable then the new one is so. Then we investigate the stability of converted new ...