Wrap-around partitioning for block bidiagonal linear systems

A stable vector algorithm for the solution of block diagonallinear systems is obtained by a permutation of the unknownscalled wrap-around partitioning combined with standard QR factorization.Wrap-around partitioning uses blocking and selects the unknownsin the blocks in turns. After a suitable orthogonal eliminationstep one ends up with a reduced system which is again blockbidiagonal and so wrap-around partitioning can be applied again.Using a simple model for vectorization overhead it is shownthat small block sizes give best performance. The minimal blocksize 2, which corresponds to cyclic reduction, is suboptimaldue to memory bank conflicts.