Parallel algorithms for solving tridiagonal and near-circulant systems

摘要

Many problems in mathematics and applied science lead to the solution of linear systems having circulant coefficient matrices. This paper presents a new stable method for the exact solution of non-symmetric tridiagonal circulant linear systems of equations. The method presented in this paper is quite competitive with Gaussian elimination both in terms of arithmetic operations and storage requirements. It is also competitive with the modified double sweep method. This method can be applied to solve the near-circulant tridiagonal system. In addition, the method is modified to allow for parallel processing.