The parallel recursive decoupling algorithm for solving tridiagonal linear systems (Q1801376)

A tridiagonal equation solver is described. The method is based on a rank-one updating strategy and the repeated partitioning of the system matrix into \(2\times 2\) submatrices. The recursive decoupling algorithm is presented. This method operates on the tridiagonal linear system, enabling the solution to be expressed in explicit form and solved independently on a multiprocessor system. It is shown that the recursive decoupling method is intrinsically parallel and can be implemented as an efficient parallel algorithm. Numerical results obtained using Balance 8000 multiprocessor system are given.