OPTIMAL 2-CYCLIC MSOR FOR BOWTIE SPECTRA AND THE CONTINUOUS MANTEUFFEL ALGORITHM

For the numerical solution of a linear system whose matrix coefficient is block 2-cyclic consistently ordered, with the eigenvalues of the a ssociated block Jacobi matrix lying in a 'bowtie'' region, several eff icient stationary iterative methods have been proposed-among others, b y Chin and Manteuffel (1988), Elman and Golub (1990), de Pillis (1991) , and Eiermann, Niethammer, and Varga (1992). We propose as an alterna tive the stationary modified successive overrelaxation (MSOR) method o r an ''equivalent'' two-step method applied to the cyclically reduced linear system. It is shown both theoretically and experimentally that the application of a ''continuous'' version of Manteuffel's algorithm to derive the optimal parameters of the two-step method produces an it erative method that is asymptotically faster than all the aforemention ed methods. (C) 1997 Elsevier Science Inc.