Rafael Lago : September 7, 2012

In this talk we present a new method for the solution of large sparse systems with multiple right hand sides, the Deflated Minimal Block Residual. This Block GMRES based method combines the best of other strategies for the solution of systems with multiple right hand sides with little extra cost and superior performance when compared to the recent published methods, as BFGMRESD and Inexact Deflation GMRES due to Robbé and Sadkane. We propose our method as a generalization of several possible block methods and discuss its main features, as monotonically decrease of the norm of block residual (thus the name of the method) and monotonically decrease of the singular values of the block residual, features that are unique to our method to the best of our knowledge. Our numerical experiments show that the method is viable even in large massively parallel computer in challenging applications as the solution of indefinite systems.