AN ANALYSIS OF THE COMPOSITE STEP BICONJUGATE GRADIENT-METHOD

The composite step biconjugate gradient method (CSBCG) is a simple mod ification of the standard biconjugate gradient algorithm (BCG) which s mooths the sometimes erratic convergence of BCG by computing only a su bset of the iterates. We show that 2 x 2 composite steps can cure brea kdowns in the biconjugate gradient method caused by (near) singularity of principal submatrices of the tridiagonal matrix generated by the u nderlying Lanczos process. We also prove a ''best approximation'' resu lt for the method. Some numerical illustrations showing the effect of roundoff error are given.