In an information explosion era, the large scale and structure complexity of datasets become problems in approximation calculation. Dynamic computing is an efficient approach to solve these problems. With the development of existing updating method applied to the dynamic approximation in multi-granular rough sets, a vector matrix based method for computing and updating approximations in Variable Precision Multi-Granulation Rough Sets (VPMGRS) was proposed. Firstly, a static algorithm for computing approximations based on vector matrix for VPMGRS was presented. Secondly, the searching area for updating approximations in VPMGRS was reconsidered, and the area was shrunk according to the properties of VPMGRS, effectively improving the time efficiency of the approximation updating algorithm. Thirdly, according to the new searching area, a vector matrix based algorithm for updating approximations in VPMGRS was proposed based on the static algorithm for computing approximations. Finally, the effectiveness of the designed algorithm was verified by experiments.

To calculate upper and lower approximations effectively and quickly under covering variation in the covering information systems, a relation matrix was defined by using the concept of characteristic function. Then the expressions for the approximations, positive, boundary and negative regions intuitively from the view of matrix were presented. Then, the expressions for the approximations, positive boundary and negative regions intuitively from the view of matrix were put forward. Furthermore, the idea of matrix was used to research and discuss the approaches for incrementally updating approximations of sets, based on the dynamic number of coverings. The investigations enriched and improved the covering rough set based dynamic learning theory and provided a method for dynamic knowledge update based in covering information systems.