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Emanuel H. Rubensson

Publications and source records attributed to Emanuel H. Rubensson.

22 records · Page 2Linked to original sources

Chunks and Tasks: a programming model for parallelization of dynamic algorithms

We propose Chunks and Tasks, a parallel programming model built on abstractions for both data and work. The application programmer specifies how data and work can be split into smaller pieces, chunks and tasks, respectively. The Chunks and Tasks library maps the chunks and tasks to physical resources. In this way we seek to combine user friendliness with high performance. An application programmer can express a parallel algorithm using a few simple building blocks, defining data and work objects and their relationships. No explicit communication calls are needed; the distribution of both work and data is handled by the Chunks and Tasks library. This makes efficient implementation of complex applications that require dynamic distribution of work and data easier. At the same time, Chunks and Tasks imposes restrictions on data access and task dependencies that facilitates the development of high performance parallel back ends. We discuss the fundamental abstractions underlying the programming model, as well as performance and fault resilience considerations. We also present a pilot C++ library implementation for clusters of multicore machines and demonstrate its performance for sparse blocked matrix-matrix multiplication.

cs.DC↗

On the condition number and perturbation of matrix functions for Hermitian matrices

Consider a matrix function f defined for Hermitian matrices. The purpose of this paper is two-fold. We derive new results for the absolute structured condition number of the matrix function and we derive new bounds for the perturbation ||f(A+E)-f(A)|| expressed in terms of eigenvalues of A and A+E. The results are general and under certain conditions hold for an arbitrary unitarily invariant matrix norm ||\cdot||. We illustrate the use of the formulas with an application to the error analysis of calculations in electronic structure theory.

math.NA↗

Non-monotonic recursive polynomial expansions for linear scaling calculation of the density matrix

As it stands, density matrix purification is a powerful tool for linear scaling electronic structure calculations. The convergence is rapid and depends only weakly on the band gap. However, as will be shown in this paper, there is room for improvements. The key is to allow for non-monotonicity in the recursive polynomial expansion. Based on this idea, new purification schemes are proposed that require only half the number of matrix-matrix multiplications compared to previous schemes. The speedup is essentially independent of the location of the chemical potential and increases with decreasing band gap.

physics.comp-ph↗

Cache oblivious storage and access heuristics for blocked matrix-matrix multiplication

We investigate effects of ordering in blocked matrix--matrix multiplication. We find that submatrices do not have to be stored contiguously in memory to achieve near optimal performance. Instead it is the choice of execution order of the submatrix multiplications that leads to a speedup of up to four times for small block sizes. This is in contrast to results for single matrix elements showing that contiguous memory allocation quickly becomes irrelevant as the blocksize increases.

cs.DS↗