A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
LAPACK's user's guide
Exploiting functional parallelism of POWER2 to design high-performance numerical algorithms
IBM Journal of Research and Development
IBM Systems Journal
Proceedings of the fourth workshop on I/O in parallel and distributed systems: part of the federated computing research conference
ScaLAPACK user's guide
The Parallel Evaluation of General Arithmetic Expressions
Journal of the ACM (JACM)
LAPACK Working Note 55: ScaLAPACK: A Scalable Linear Algebra Library for Distributed Memory Concurrent Computers
A comparison of parallel solvers for diagonally dominant and general narrow-banded linear systems
Parallel numerical linear algebra
A unified model for multicore architectures
IFMT '08 Proceedings of the 1st international forum on Next-generation multicore/manycore technologies
Cache-optimal algorithms for option pricing
ACM Transactions on Mathematical Software (TOMS)
Evaluating multicore algorithms on the unified memory model
Scientific Programming - Software Development for Multi-core Computing Systems
Upper and lower I/O bounds for pebbling r-pyramids
Journal of Discrete Algorithms
Computers & Mathematics with Applications
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This article describes the design, implementation, and evaluation of a parallel algorithm for the Cholesky factorization of symmetric banded matrices. The algorithm is part of IBM's parallel engineering and scientific subroutine library version 1.2 and is compatible with ScaLAPACK's banded solver. Analysis, as well as experiments on an IBM SP2 distributed-memory parallel computer, shows that the algorithm efficiently factors banded matrices with wide bandwidth. For example, a 31-mode SP2 factors a large matrix more than 16 times faster than a single node would factor it using the best sequential algorithm, and more than 20 times faster than a single node would using LAPACK's DPBTRF. The algorithm uses novel ideas in the area of distributed dense-matrix computations that include the use of a dynamic schedule for a blocked systolic-like algorithm and the separation of the input and output layouts from the layout the algorithm uses internally. The algorithm alson uses known techniques such as blocking to improve its communication-to-computation ratio and its data-cache behavior.