Thesymmetriclinearsystemgivesusmanysimplificationsandapossibilitytoadaptthecomputationstothecomputerathandinordertoachievebetterperformance.TheaimofthispaperistoconsidertheblockbidiagonalizationmethodsderivedfromasymmetricaugmentedmultiplelinearsystemsandmakeacomparisonwiththeblockGMRESandblockbiconjugategradientmethods.