Anadaptivealgorithmforsolvinglargenonsymmetriclinearsystemsispresentedinthispaper.ThenewalgorithmcombinespolynomialpreconditioningtechniquewiththeCGNRmethod.Residualpolynomialisusedinthepreconditioningtoestimatetheeigenvaluesofthes.p.d.matrixArA,andtheresidualpolynomialisgeneratedfromseveralstepsofCGNRbyrecurrence.Thealgorithmisadaptiveduringitsimplementation.Therobustnessismaintained,andtheiterationconvergenceisspeededup.Twonumericaltestresultsarealsoreported.
