The computation and communication complexity of a parallel banded system solver
ACM Transactions on Mathematical Software (TOMS)
Direct methods for sparse matrices
Direct methods for sparse matrices
Efficient Tridiagonal Solvers on Multicomputers
IEEE Transactions on Computers
Application and accuracy of the parallel diagonal dominant algorithm
Parallel Computing
A Fast Direct Solution of Poisson's Equation Using Fourier Analysis
Journal of the ACM (JACM)
A Parallel Method for Tridiagonal Equations
ACM Transactions on Mathematical Software (TOMS)
Parallel Computers 2: Architecture, Programming, and Algorithms
Parallel Computers 2: Architecture, Programming, and Algorithms
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A new method, namely the Parallel Two-Level Hybrid (PTH) method, is developed to solve tridiagonal systems on parallel computers. PTH is designed based on Parallel Diagonal Dominant (PDD) algorithm. Like PDD, PTH is highly scalable. It provides accurate solutions when PDD may not be applicable and maintains a near PDD performance when the underlying machine ensemble size is large. By controlling its two-level partition, PTH can deliver optimal performance for different machine ensemble and problem sizes. Theoretical analyses and numerical experiments indicate that PTH is significantly better than existing methods for many scientific and engineering applications.