Analyzing Scalability of Neville Elimination

The scalability of a parallel system is a measure of its capacity to effectively use an increasing number of processors. Several performance evaluation metrics have been developed to study the scalability of parallel algorithms and architectures. The isoefficiency function is one of those metrics. It relates the size of the problem being solved to the number of processors required to maintain efficiency at a fixed value. This work studies the scalability of Neville elimination, which is a method to solve a linear equation system. This process appears naturally when the Neville strategy of interpolation is used to solve linear systems. The scalability behavior of some algorithms of this method is studied on an IBM SP2 and also over a network of personal computers using the isoefficiency function and the scaled efficiency.

[1]  Report,et al.  Public International Benchmarks for Parallel Computers , 1993 .

[2]  N. Higham.  Bounding the error in Gaussian Elimination for Tridiagonal systems , 1990 .

[3]  Juan Manuel Peña,et al.  Scaled pivoting in Gauss and Neville elimination for totally positive systems , 1993 .

[4]  Vipin Kumar,et al.  Introduction to Parallel Computing , 1994 .

[5]  Jing Yuan,et al.  Performance and scalability of MPI on PC clusters , 2004, Concurr. Comput. Pract. Exp..

[6]  G. Amdhal,et al.  Validity of the single processor approach to achieving large scale computing capabilities , 1967, AFIPS '67 (Spring).

[7]  Juan Manuel Peña,et al.  Backward error analysis of Neville elimination , 1997 .

[8]  José Ranilla,et al.  A Columnwise Block Striping in Neville Elimination , 2001, PPAM.

[9]  Juan Manuel Peña,et al.  Total positivity and Neville elimination , 1992 .

[10]  José Ranilla,et al.  A study of the performance of Neville elimination using two kinds of partitioning techniques , 2001 .

[11]  Juan Manuel Peña,et al.  A matricial description of Neville elimination with applications to total positivity , 1994 .

[12]  Vijay P. Kumar,et al.  Analyzing Scalability of Parallel Algorithms and Architectures , 1994, J. Parallel Distributed Comput..

[13]  Francisco Tirado,et al.  A parallel multigrid solver for viscous flows on anisotropic structured grids , 2003, Parallel Comput..

[14]  Charles A. Micchelli,et al.  Total positivity and its applications , 1996 .

[15]  Michael W. Berry,et al.  Public international benchmarks for parallel computers: PARKBENCH committee: Report-1 , 1994 .