Diagonal Dominance in the Parallel Partition Method for Tridiagonal Systems
Chris H. Walshaw · SIAM Journal on Matrix Analysis and Applications · 1995
The partition method for the parallel solution of tridiagonal linear systems is discussed and the coefficients of the reduced global system derived. It is shown that if the full system is diagonally dominant then the reduced system retains this property. This has important implications for the stability of calculations in this reduced system and eliminates the need for global pivoting with its expensive communication overhead.