A weighted Jacobi smoother-based algebraic technique is proposed for smoothing discrete data, e.g., signal, image or video on grids with arbitrary topology. The energy of discrete data is defined in H 1 -space and a requirement for discrete scale-space theory is suggested based on the non-increase of energetic norm of the data. A shape-preserving smoothing method is also derived using a combination of Jacobi smoothers. Scale-selective smoothing of the data is achieved by eigen-analysis of the stiffness matrix. Experimental results are shown for isotropic image data.