The support vector machine (SVM) is a supervised learning algorithm used in a variety of applications, including robust target classification. The SVM training problem can be formulated as dense quadratic programming problem (QP). In practice, this QP is solved in batch mode, using general-purpose interior-point solvers. Although quite efficient, these implementations are not well suited in situations where the training vectors are made available sequentially. In this paper we discuss a recursive algorithm for SVM training. The algorithm is based on efficient updates of approximate solutions on the dual central path of the QP and can be analyzed using the convergence theory recently developed for interior-point methods. The idea is related to cutting-plane methods for large-scale optimization and sequential analytic centering techniques used successfully in set-membership estimation methods in signal processing.