Railway computation for infinite linear systems

The problem of solving an infinite system of linear equations finitely expressed is addressed. Modifications of the Gauss-Seidel method are presented, especially suitable for the implementation on SMP machines with a small number of processors. One of the proposed parallel algorithms, which concentrates the computational efforts where they are most neeeded, results to be more efficient than the sequential algorithm, even from the point of view of the total number of operations

Timing models and local stopping criteria for asynchronous iterative algorithms

Asynchronous iterative algorithms can reduce much of the data dependencies associated with synchronization barriers. The reported study investigates the potentials of asynchronous iterative algorithms by quantifying the critical parallel processing factors. Specifically, a time complexity-based analysis method is used to understand the inherent interdependencies between computing and communication overheads for the parallel asynchronous algorithm. The results show, not only that the computational experiments closely match the analytical results, but also that the use of asynchronous iterative algorithms can be beneficial for a vast number of parallel processing environments. The choice of local stopping criteria that is critically important to the overall system performance is investigated in depth. 1999 Academic Press Key Words: timing models; asynchronous algorithms; parallel iterative methods

Asynchronous and Multiprecision Linear Solvers - Scalable and Fault-Tolerant Numerics for Energy Efficient High Performance Computing

Asynchronous methods minimize idle times by removing synchronization barriers, and therefore allow the efficient usage of computer systems. The implied high tolerance with respect to communication latencies improves the fault tolerance. As asynchronous methods also enable the usage of the power and energy saving mechanisms provided by the hardware, they are suitable candidates for the highly parallel and heterogeneous hardware platforms that are expected for the near future