This paper is devoted to subgrid scale models in the numerical solution of partial differential equations that involve information on different scales. To derive this model a wavelet-based method is used. The authors discuss different compact representations of the homogenized operator and show how to improve the efficiency of certain wavelet-based homogenization algorithms. The method suggested in this work becomes particularly simple in two dimensions when it is difficult to find the divergence form of the Schur complement. Some theoretical aspects of the method are demonstrated for a one-dimensional elliptic problem on an infinite domain. The performance of the method suggested is demonstrated on the following examples: a one dimensional elliptic problem with discontinuous or random coefficients, a Helmholtz equation in one and two dimensions, and one-dimensional hyperbolic problems with variable coefficients.