Divide and conquer for the solution of banded linear systems of equations

摘要

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.