Despite the promise of extremely efficient matrix-vector multiplication (MVM) by ReRAM crossbar arrays (RCAs), maintaining high accuracy has been challenging due to nonidealities such as wire resistance (also known as IR drop) and I-V nonlinearity (i.e., voltage-dependent conductance). For system architects, a fast method to accurately predict the MVM output of an RCA under nonidealities is highly desirable. While IR drop alone without I-V nonlinearity can be efficiently predicted, the existence of I-V nonlinearity makes the problem much harder. In this paper we propose a novel algorithm based on iterative refinement, which can predict with high accuracy the outcome of an MVM operation on an RCA in the presence of both I-V nonlinearity and IR drop. Our experiments using binary RCAs of different sizes demonstrate that our proposed method is order-of-magnitude more accurate than previous methods in terms of RMS error. We also present case studies predicting hardware-realistic accuracy of binarized neural networks on RCAs as well as nonideality-aware retraining, demonstrating the efficacy of our method for early design space exploration of ReRAM-based accelerators.