Parallel Solution to BlockTridiagonal Linear Equations by Twolayer Mixedblock Algorithm
Abstract
A novel scalable parallel algorithm, PTHB, is proposed to solve blocktridiagonal equations with strict block diagonal dominant based on the idea of Sun's about PTH method. By precision analysis, divideconquer strategy is obtained ensuring the accuracy and optimal efficiency. PTHB provides an approximate solution that is equivalent to the exact solution within machine accuracy. The method has been implemented on the "ZiQiang 3000" supercomputer of Shanghai University.The numerical results are the same with the theoretical analysis. With the given the accuracy, the linear speedup rate is obtained, and parallel efficiency over 90% is reached.
 Publication:

Numerical Analysis and Applied Mathematics ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics
 Pub Date:
 September 2011
 DOI:
 10.1063/1.3637805
 Bibcode:
 2011AIPC.1389.1102Z
 Keywords:

 computer science;
 supercomputers;
 subroutines;
 matrix algebra;
 89.20.Ff;
 07.05.Bx;
 02.60.Gf;
 02.10.Yn;
 Computer science and technology;
 Computer systems: hardware operating systems computer languages and utilities;
 Algorithms for functional approximation;
 Matrix theory