论文信息 - A divide-and-conquer method of solving tridiagonal systems on hypercube massively parallel computers

A divide-and-conquer method of solving tridiagonal systems on hypercube massively parallel computers

The authors present a new parallel algorithm, based on the divide-and-conquer (DC) strategy, for solving tridiagonal systems. Through a comparative study between their DC method and other well known tridiagonal solvers: cyclic odd-even reduction (CR), recursive doubling (RD), and the partition method, they show that for the binary hypercube architecture, the communication complexity of their DC method is the lowest among all, and therefore the most efficient tridiagonal solver for communication-expensive massively parallel hypercube computers.<<ETX>>

Xiaojing Wang | Z.G. Mou | Z. G. Mou | Xiaojing Wang

[1] Z. G. Mou,et al. Divacon: a parallel language for scientific computing based on divide-and-conquer , 1990, [1990 Proceedings] The Third Symposium on the Frontiers of Massively Parallel Computation.

[2] Harold S. Stone,et al. An Efficient Parallel Algorithm for the Solution of a Tridiagonal Linear System of Equations , 1973, JACM.

[3] Zhijing George Mou. A formal model for divide-and-conquer and its parallel realization , 1990 .

[4] S. Johnsson. Solving tridiagonal systems on ensemble architectures , 1987 .

[5] Roger W. Hockney,et al. A Fast Direct Solution of Poisson's Equation Using Fourier Analysis , 1965, JACM.

[6] R. Hockney. The potential calculation and some applications , 1970 .

[7] Chris R. Jesshope,et al. Parallel Computers 2: Architecture, Programming and Algorithms , 1981 .

[8] John N. Tsitsiklis,et al. Parallel and distributed computation , 1989 .

[9] Harold S. Stone,et al. Parallel Tridiagonal Equation Solvers , 1975, TOMS.

[10] Swarn P. Kumar,et al. Solving Tridiagonal Linear Systems On the Butterfly Parallel Computer , 1989, Int. J. High Perform. Comput. Appl..

[11] S. K. Dhall,et al. Analysis and Design of Parallel Algorithms: Arithmetic and Matrix Problems , 1990 .