A parallel method for linear equations with tridiagonal Toeplitz coefficient matrices

High Performance Portable Solver for Tridiagonal Toeplitz Systems of Linear Equations

“…There are several methods for solving such systems (the review of the literature can be found in [ 5 ]). Rojo [ 10 ] proposed a method for solving symmetric tridiagonal Toeplitz systems using LU decomposition of a system with almost Toeplitz structure together with Sherman-Morrison’s formula and this approach was modified to obtain new solvers for a possible parallel execution [ 7 , 9 ].…”

Solving tridiagonal Toeplitz systems of linear equations on GPU‐accelerated computers

“…The basic approach comes from Rojo, 8 who proposed a method using LU decomposition of a system with almost Toeplitz structure together with Sherman–Morrison's formula. This approach was modified to obtain new solvers with the possibility of parallel execution 9,10 …”

“…This approach was modified to obtain new solvers with the possibility of parallel execution. 9,10 Recently, 7 we proposed a new divide and conquer parallel algorithm for solving tridiagonal Toeplitz systems of linear equations with diagonally dominant matrices using the splitting T = LR + P, where L, R are bidiagonal matrices and P has only one nonzero entry. We showed how to reduce the number of necessary synchronizations and use SIMD extensions of modern processors 11,12 to achieve reasonable performance.…”

Fast solvers for tridiagonal Toeplitz linear systems

“…Tridiagonal Toeplitz linear systems have their own applications in mathematical science and engineering field (Noschese et al 2013;Rojo 1990;Saad 2003). Due to their special structure, fast and/or accurate solvers have intrigued researchers for decades, see for example (Yan and Chung 1994;Terekhov 2015;Du et al 2017;Rojo 1990) for serial algorithms and (Garey and Shaw 2001;Kim 1990;McNally et al 2000) for parallel algorithms. Those algorithms are all numerically reliable, if the coefficient matrix A is strictly diagonally dom-inant.…”