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This paper concerns an iterative technique for solving discretized Stokes-type equations with varying viscosity coefficient. We build a special block preconditioner for the discrete system of equations and perform an analysis revealing its properties; the theoretical analysis is based on the weighted Nečas inequality. The subject of this paper is motivated by numerical solution of incompressible non-Newtonian fluid equations. In particular, the general analysis is applied to the linearizeddoi:10.1137/08744803 fatcat:6zdiublacfcmbhsjymx3oly65y