The computation and communication complexity of a parallel banded system solver
ACM Transactions on Mathematical Software (TOMS)
Solving tridiagonal systems on ensemble architectures
SIAM Journal on Scientific and Statistical Computing
Scientific computing on vector computers
Scientific computing on vector computers
Introduction to Parallel & Vector Solution of Linear Systems
Introduction to Parallel & Vector Solution of Linear Systems
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
A new class of parallel algorithms for solving linear tridiagonal systems
ACM '86 Proceedings of 1986 ACM Fall joint computer conference
Parallel Tridiagonal Equation Solvers
ACM Transactions on Mathematical Software (TOMS)
The Solution of Tridiagonal Linear Systems on the CDC STAR 100 Computer
ACM Transactions on Mathematical Software (TOMS)
A Parallel Method for Tridiagonal Equations
ACM Transactions on Mathematical Software (TOMS)
Vector Fortran for numerical problems on CRAY-1
Communications of the ACM
CONPAR 90/VAPP IV Proceedings of the Joint International Conference on Vector and Parallel Processing
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We describe a divide and conquer algorithm which solves linear tridiagonal systems with one right-hand side, especially suited for parallel computers. The algorithm is flexible, permits multiprocessing or a combination of vector and multiprocessor implementations, and is adaptable to a wide range of parallelism granularities. This algorithm can also be combined with recursive doubling, cyclic reduction or Wang's partition method, in order to increase the degree of parallelism and vectorizability. The divide and conquer method will be explained. Some results of time measurements on a CRAY X-MP/28, on an Alliant FX/8, and on a Sequent Symmetry S81b, as well as comparisons with the cyclic reduction algorithm and Gaussian elimination will be presented. Finally, numerical results are given.