VIRTUAL-RESIDUAL PRECONDITIONING

Sergey Fomel has developed a wholly different approach to preconditioning to that described above. He calls his method the ``model-extension'' method. I call it the ``virtual-residual'' method. Both names are suggestive of the method. Fomel's preconditioning method depends on some fundamental facts from the theory of least squares. I establish only one of them here before presenting his algorithm.