Learning from Demonstration (LfD) has been identified as an effective method for making robots more flexible not only on manufacturing production lines, but also in houses, schools or hospitals. Most importantly, it enables the robot to generalize to similar but slightly distinct tasks. In spite of the convenience and flexibility of such a methodology, it inherently incorporates the dilemma of accuracy and stability, which is mainly owing to the fact that stable dynamical systems potentially result in a poor reproduction performance. This paper presents a learning approach to model robot point-to-point (also known as discrete or reaching) movements from demonstrations with autonomous dynamical systems. To solve the emphasized accuracystability dilemma in the current work, we propose a learning approach based on dimension ascending. In this way, the robot is able to learn the parameters of the dynamical systems and meanwhile ensures that all motions closely follow the demonstrations while ultimately reaching and stopping at the target.