The computation and communication complexity of a parallel banded system solver
ACM Transactions on Mathematical Software (TOMS)
ScaLAPACK user's guide
On Stable Parallel Linear System Solvers
Journal of the ACM (JACM)
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
A Comparison of Parallel Solvers for Diagonally Dominant and General Narrow-Banded Linear Systems II
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Parallel Algorithms on the CEDAR System
CONPAR '86 Conference on Algorithms and Hardware for Parallel Processing
Implementation in ScaLAPACK of Divide-and-Conquer Algorithms forBanded and Tridiagonal Linear Systems
Subband decomposition approach for the simulation of quantum electron transport in nanostructures
Journal of Computational Physics
Analyzing memory access intensity in parallel programs on multicore
Proceedings of the 22nd annual international conference on Supercomputing
A multi-level parallel simulation approach to electron transport in nano-scale transistors
Proceedings of the 2008 ACM/IEEE conference on Supercomputing
A Parallel Sparse Linear Solver for Nearest-Neighbor Tight-Binding Problems
Euro-Par '08 Proceedings of the 14th international Euro-Par conference on Parallel Processing
A tearing-based hybrid parallel banded linear system solver
Journal of Computational and Applied Mathematics
PSPIKE: A Parallel Hybrid Sparse Linear System Solver
Euro-Par '09 Proceedings of the 15th International Euro-Par Conference on Parallel Processing
A compiler-automated array compression scheme for optimizing memory intensive programs
Proceedings of the 24th ACM International Conference on Supercomputing
A tearing-based hybrid parallel sparse linear system solver
Journal of Computational and Applied Mathematics
Weighted Matrix Ordering and Parallel Banded Preconditioners for Iterative Linear System Solvers
SIAM Journal on Scientific Computing
A parallel numerical solver using hierarchically tiled arrays
LCPC'10 Proceedings of the 23rd international conference on Languages and compilers for parallel computing
Performance models for the Spike banded linear system solver
Scientific Programming
A numerical scheme for particle-laden thin film flow in two dimensions
Journal of Computational Physics
A domain-decomposing parallel sparse linear system solver
Journal of Computational and Applied Mathematics
A parallel sparse algorithm targeting arterial fluid mechanics computations
Computational Mechanics
A threaded SPIKE algorithm for solving general banded systems
Parallel Computing
Parallel solution of narrow banded diagonally dominant linear systems
PARA'10 Proceedings of the 10th international conference on Applied Parallel and Scientific Computing - Volume 2
A scalable, numerically stable, high-performance tridiagonal solver using GPUs
SC '12 Proceedings of the International Conference on High Performance Computing, Networking, Storage and Analysis
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
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This paper describes an efficient and robust hybrid parallel solver ''the SPIKE algorithm'' for narrow-banded linear systems. Two versions of SPIKE with their built-in-options are described in detail: the Recursive SPIKE version for handling non-diagonally dominant systems and the Truncated SPIKE version for diagonally dominant ones. These SPIKE schemes can be used either as direct solvers, or as preconditioners for outer iterative schemes. Both versions are faster than the direct solvers in ScaLAPACK on parallel computing platforms, and quite competitive in terms of achieved accuracy for handling systems that are dense within the band.