Support vector machine (SVM) has shown great potential in pattern recognition and regressive estimation. Due to the industrial development demands, such as the fermentation process modeling, improving the training performance on increasingly large sample sets is an important problem. However, solving a large optimization problem is computationally intensive and memory intensive. In this paper, a geometric interpretation of SVM regression (SVR) is derived, and mu-SVM is extended for both L-1-norm and L-2-norm penalty SVR. Further, Gilbert algorithm, a well-known geometric algorithm, is modified to solve SVR problems. Theoretical analysis indicates that the presented SVR training geometric algorithms have the same convergence and almost identical cost of computation as their corresponding algorithms for SVM classification. Experimental results show that the geometric methods are more efficient than conventional methods using quadratic programming and require much less memory.