In this paper, we propose efficient computational scheduling of box and Gaussian filtering. These filters are fundamental tools and used for various applications. The computational order of the naïve implementations of these FIR filters are $O(r^{2})$, where $r$ is the kernel radius. A separable implementation reduces the order into $O(r)$ but requires twice times of filtering. A recursive representation dramatically sheds the order into $O(1)$ but also needs twice or more times filtering. The efficient representation curtails the number of arithmetic operations; however, the influence of data I/O for the computational time becomes dominant. In this paper, we optimize the computational scheduling of $O(1)$ box and Gaussian filters to competently utilize cache memory for reducing the computational time of data I/O. Experimental results show that the proposed scheduling has higher computational performance than the conventional implementation.