Parallel methods for tridiagonal equations (Q1106618)

The authors present parallel adaptations of the Gauss-Seidel iterative method for solving tridiagonal systems of linear algebraic equations. Two of them possess a similarity to the marching principle developed previously for solving block-tridiagonal systems arising in the numerical solution of partial differential equations while the third one is based on the red-black ordering of the unknowns. The computational work is distributed proportionally among slave processors of the parallel system considered, yielding almost optimal speed-up values. The methods are compared from a point of view of the number of arithmetic and communication operations required. Through the parallelization a convergence property of the original methods is preserved. The experience achieved by the simulation can be applied also to other parallel MIMD-type computer configurations.