| Abstract: | With the aid of index functions, we re-derive the ML($n$)BiCGStab algorithm
in Yeung and Chan, SIAM J. Sci. Comput., 21 (1999), pp. 1263-1290] systematically.
There are $n$ ways to define the ML($n$)BiCGStab residual vector. Each definition leads
to a different ML($n$)BiCGStab algorithm. We demonstrate this by presenting a second
algorithm which requires less storage. In theory, this second algorithm serves as a
bridge that connects the Lanczos-based BiCGStab and the Arnoldi-based FOM while
ML($n$)BiCG is a bridge connecting BiCG and FOM. We also analyze the breakdown
situation from the probabilistic point of view and summarize some useful properties of
ML($n$)BiCGStab. Implementation issues are also addressed. |
