A Parallel Solver for Circulant Toeplitz Tridiagonal Systems on Hypercubes

[[abstract]]Solving circulant Toeplitz tridiagonal systems arises in many engineering applications. This paper presents a fast parallel algorithm for solving this type of systems. The number of floating-point operations required in our algorithm is less than the previous parallel algorithm [cf. Kim and Lee (1990)] for solving the similar system. Specifically, an overlapping technique is proposed to reduce the communication steps required. In addition, an error analysis is given. The implementation of our algorithm on the nCUBE2/E with 16 processors has been carried out. The experimental results show that the speedup is almost linearly proportional to the number of processors.