Abstract: Granular-ball generation (GBG) serves as the foundation for various learning tasks in granular-ball computing (GBC), such as classification and clustering. However, existing adaptive GBG methods introduce significant uncertainty due to the strategy of randomly selecting the division center, resulting in a highly unstable granular-ball classification result. Moreover, the k-division based adaptive GBG method requires repeated overlap detection and de-overlapping of granular balls, which significantly increases the computational overhead during the iterative process and impairs the efficiency of GBG. To address the above issues, a new method for stable, accelerated and adaptive GBG (SAAGBG) is proposed in this paper, building upon the existing k-division strategy. On the one hand, SAAGBG selects the sample point with the smallest difference with the median vector of the data cluster as the division center, which effectively enhances the robustness to outliers and avoids the inconsistency and instability caused random center selection. On the other hand, a new adaptive division condition based on granular-ball coverage is introduced into SAAGBG, which replaces the minimum quality threshold and overlap detection steps in the original k-division based GBG method, significantly improving the efficiency of the GBG process. Experimental results on benchmark datasets and datasets with varying noise ratios demonstrate that SAAGBG achieves greater stability and efficiency without loss of classification accuracy compared to the mainstream adaptive GBG methods.