A comparison of parallel solvers for diagonally dominant and general narrow-banded linear systems
Parallel numerical linear algebra
A Comparison of Parallel Solvers for Diagonally Dominant and General Narrow-Banded Linear Systems II
Euro-Par '99 Proceedings of the 5th International Euro-Par Conference on Parallel Processing
Domain decomposition solution of nonlinear two-dimensional parabolic problems by random trees
Journal of Computational Physics
EURASIP Journal on Advances in Signal Processing - Special issue on advanced equalization techniques for wireless communications
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An algorithm for the solution of banded linear systems is presented and discussed which combines stability with scalability. This is achieved by implementing divide and conquer for Gaussian elimination with partial pivoting. Earlier divide and conquer algorithms for Gaussian elimination have problems with instabilities and can even break down as they implement a more restricted form of pivoting.The key observation used for the implementation is the invariance of LU factorization with partial pivoting under permutations. Theoretical analysis shows that the algorithm has low redundancy, a high degree of parallelism and relatively low communication.