===affil2: ===firstname: James ===firstname4: ===firstname3: ===lastname2: ===lastname: Brannick ===firstname5: ===affil6: ===lastname3: ===email: brannick@psu.edu ===lastname6: ===affil5: ===otherauths: ===lastname4: ===affil4: ===lastname7: ===affil7: ===firstname7: ===postal: 311 McAllister Bldg. Department of Mathematics Penn State University University Park, PA 16803 ===firstname6: ===ABSTRACT: In this talk, we review the idea of Compatible Relaxation (CR) as a tool for coupling the choice of the coarse variables with the MG relaxation scheme. We then develop an algorithm that uses CR to iteratively update the set of coarse variables as well as the relaxation scheme. ===affil3: ===lastname5: ===affilother: ===title: Compatible Relaxation ===firstname2: