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A power allocation or scheduling problem is studied for a multiuser multiple-input multiple-output (MIMO) wireless relay system where there is a non-regenerative relay between one access point and multiple users. Each node in the system is equipped with multiple antennas. The purpose of this study is to develop fast algorithms to compute the source covariance matrix (or matrices) and the relay transformation matrix to optimize a system performance. We consider the minimization of power consumption subject to rate constraint and also the maximization of system throughput subject to power constraint. These problems are nonconvex and apparently have no simple solutions. In this paper, a number of computational strategies are presented and their performances are investigated. Both uplink and downlink cases are considered. The use of multiple carriers is also discussed. Moreover, a generalized water-filling (GWF) algorithm is developed to solve a special class of convex optimization problems. The GWF algorithm is used for two of the strategies shown in this paper.