Solving tridiagonal systems on ensemble architectures
SIAM Journal on Scientific and Statistical Computing
The algebraic eigenvalue problem
The algebraic eigenvalue problem
Cyclic Reduction for Special Tridiagonal Systems
SIAM Journal on Matrix Analysis and Applications
The parallel QR factorization algorithm for tridiagonal linear systems
Parallel Computing
A tridiagonal solver for massively parallel computers
Advances in Engineering Software - Special issue; special issue on large-scale analysis and design on high-performance computers and workstations
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
Developments and trends in the parallel solution of linear systems
Parallel Computing - Special Anniversary issue
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)
Parallel-Vector Equation Solvers for Finite Element Engineering Applications
Parallel-Vector Equation Solvers for Finite Element Engineering Applications
Accuracy and Stability of Numerical Algorithms
Accuracy and Stability of Numerical Algorithms
Optimal and efficient parallel tridiagonal solvers using direct methods
The Journal of Supercomputing - Special issue: Parallel and distributed processing and applications
A class of novel parallel algorithms for the solution of tridiagonal systems
Parallel Computing
Influence of Preconditioning and Blocking on Accuracy in Solving Markovian Models
International Journal of Applied Mathematics and Computer Science
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We present a matrix factorization called WZ factorization for the solution of symmetric tridiagonal linear systems. When combined with partitioning scheme, it renders a divide and conquer algorithm. Existence theorems are presented and backward error analysis is given. A variant of WZ factorization called WDZ factorization is also presented. Both WZ and WDZ algorithms for parallel solution of large tridiagonal symmetric positive definite linear systems are implemented on parallel machine with MPI as inter node communication.