Comparison of several iterative techniques in the solution of symmetric banded equations on a two-pipe cyber 205

摘要

The effectiveness of several iterative techniques for solving matrix equations resulting from finite-difference approximations to self-adjoint parabolic and elliptic partial differential equations is investigated: the strongly implicit procedure (sip), the incomplete Cholesky conjugate-gradient method (iccg), the vectorized iccg (viccg), the modified iccg (miccg), the diagonally scaled conjugate-gradient method (dscg), the polynomial preconditioned conjugate-gradient method. (polcg), and the polynomial form of iccg (piccg). The comparison is made on a vector machine (two-pipe Cyber 205) where vectorization of the code is done primarily by the vector compiler available. It is found that of the methods studied, polcg and miccg appear to require the least amount of CPU time. An advantage of miccg over polcg is that it is less sensitive to increasing matrix size. Its disadvantages are that it requires an iteration parameter, has a greater setup time, and needs more storage than polcg.