ACM Transactions on Mathematical Software (TOMS)
Compiling techniques for first-order liner recurrences on a Vector computer
Proceedings of the 1988 ACM/IEEE conference on Supercomputing
Prefix algorithms for tridiagonal systems on hypercube multiprocessors
C3P Proceedings of the third conference on Hypercube concurrent computers and applications - Volume 2
A Parallel Algorithm for Solving Sparse Triangular Systems
IEEE Transactions on Computers
Efficient Tridiagonal Solvers on Multicomputers
IEEE Transactions on Computers
Vectorized algorithm for B-spline curve fitting on Cray X-MP EA/16se
Proceedings of the 1992 ACM/IEEE conference on Supercomputing
A generalized vision of some parallel bidiagonal systems solvers
ICS '94 Proceedings of the 8th international conference on Supercomputing
Unified Architecture for Divide and Conquer Based Tridiagonal System Solvers
IEEE Transactions on Computers
Prefix Computations on a Generalized Mesh-Connected Computer with Multiple Buses
IEEE Transactions on Parallel and Distributed Systems
Efficient parallel solutions of linear algebraic circuits
Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Parallel algorithms for solution of tridiagonal systems on multicomputers
ICS '89 Proceedings of the 3rd international conference on Supercomputing
Accelerated Iterative Methods for the Solution of Tridiagonal Systems on Parallel Computers
Journal of the ACM (JACM)
The Complexity of Parallel Evaluation of Linear Recurrences
Journal of the ACM (JACM)
On Stable Parallel Linear System Solvers
Journal of the ACM (JACM)
Odd-Even Reduction for Banded Linear Equations
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)
Associative and Parallel Processors
ACM Computing Surveys (CSUR)
A Survey of Parallel Machine Organization and Programming
ACM Computing Surveys (CSUR)
ACM Transactions on Programming Languages and Systems (TOPLAS)
Vector Fortran for numerical problems on CRAY-1
Communications of the ACM
Efficient parallel algorithms for some graph problems
Communications of the ACM
Parallel Solutions of Simple Indexed Recurrence Equations
IEEE Transactions on Parallel and Distributed Systems
Optimal and efficient algorithms for summing and prefix summing on parallel machines
Journal of Parallel and Distributed Computing
Parallel Minimal Norm Method for Tridiagonal Linear Systems
IEEE Transactions on Computers
A note on the recursive decoupling method for solving tridiagonal linear systems
Applied Mathematics and Computation
A scalable parallel algorithm for periodic symmetric Toeplitz tridiagonal systems
Progress in computer research
Parallel Solutions of Indexed Recurrence Equations
IPPS '97 Proceedings of the 11th International Symposium on Parallel Processing
The complexity of parallel evaluation of linear recurrence
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
New algorithms and lower bounds for the parallel evaluation of certain rational expressions
STOC '74 Proceedings of the sixth annual ACM symposium on Theory of computing
IEEE Transactions on Parallel and Distributed Systems
Efficient parallel solutions of linear algebraic circuits
Journal of Parallel and Distributed Computing
A cost-optimal parallel implementation of a tridiagonal system solver using skeletons
Future Generation Computer Systems - Special issue: Parallel computing technologies
A parallel priority queueing system with finite buffers
Journal of Parallel and Distributed Computing
A class of novel parallel algorithms for the solution of tridiagonal systems
Parallel Computing
Parallel computing in Asian option pricing
Parallel Computing
Graph transformation and designing parallel sparse matrix algorithms beyond data dependence analysis
Scientific Programming - Distributed Computing and Applications
Implementation of Permutation Functions in Illiac IV-Type Computers
IEEE Transactions on Computers
IEEE Transactions on Computers
The Future of Parallel Processing
IEEE Transactions on Computers
Fast problem-size-independent parallel prefix circuits
Journal of Parallel and Distributed Computing
International Journal of Computer Mathematics
A Parallel Algorithm for the Efficient Solution of a General Class of Recurrence Equations
IEEE Transactions on Computers
Parallel solution of recurrence problems
IBM Journal of Research and Development
Fast tridiagonal solvers on the GPU
Proceedings of the 15th ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming
A cost-optimal parallel implementation of a tridiagonal system solver using skeletons
Future Generation Computer Systems - Special issue: Parallel computing technologies
NPC'07 Proceedings of the 2007 IFIP international conference on Network and parallel computing
Journal of Computational Physics
On unlimited parallelism of DSP arithmetic computations
ICASSP'93 Proceedings of the 1993 IEEE international conference on Acoustics, speech, and signal processing: plenary, special, audio, underwater acoustics, VLSI, neural networks - Volume I
Automatic parallelization via matrix multiplication
Proceedings of the 32nd ACM SIGPLAN conference on Programming language design and implementation
GPU-efficient recursive filtering and summed-area tables
Proceedings of the 2011 SIGGRAPH Asia Conference
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
Journal of Parallel and Distributed Computing
Fast poisson solvers for graphics processing units
PARA'12 Proceedings of the 11th international conference on Applied Parallel and Scientific Computing
| Hi-index | 0.06 |
Tridiagonal linear systems of equations can be solved on conventional serial machines in a time proportional to N, where N is the number of equations. The conventional algorithms do not lend themselves directly to parallel computation on computers of the ILLIAC IV class, in the sense that they appear to be inherently serial. An efficient parallel algorithm is presented in which computation time grows as log2 N. The algorithm is based on recursive doubling solutions of linear recurrence relations, and can be used to solve recurrence relations of all orders.