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In this paper, regularization path algorithms were proposed as a novel approach to the model selection problem by exploring the path of possibly all solutions with respect to some regularization hyperparameter in an efficient way. This approach was later extended to a support vector regression (SVR) model called epsiv -SVR. However, the method requires that the error parameter epsiv be set a priori. This is only possible if the desired accuracy of the approximation can be specified in advance. In this paper, we analyze the solution space for epsiv-SVR and propose a new solution path algorithm, called epsiv-path algorithm, which traces the solution path with respect to the hyperparameter epsiv rather than lambda. Although both two solution path algorithms possess the desirable piecewise linearity property, our epsiv-path algorithm overcomes some limitations of the original lambda-path algorithm and has more advantages. It is thus more appealing for practical use.