In this paper we develop the Generalised Recombination Interpolation Method (GRIM) for finding sparse approximations of functions initially given as linear combinations of some (large) number of simpler functions. GRIM is a hybrid of dynamic growth-based interpolation techniques and thinning-based reduction techniques. We establish that the number of non-zero coefficients in the approximation returned by GRIM is controlled by the concentration of the data. In the case that the functions involved are Lip$(\gamma)$ for some $\gamma > 0$ in the sense of Stein, we obtain improved convergence properties for GRIM. In particular, we prove that the level of data concentration required to guarantee that GRIM finds a good sparse approximation is decreasing with respect to the regularity parameter $\gamma > 0$.

翻译：在本文中,我们开发了普遍重组内插方法(GRIM),以寻找最初作为某些(大)较简单的功能的线性组合而提供的功能的微弱近似值。GRIM是动态增长型内插技术和减薄型减少技术的混合体。我们确定,GRIM返回的近似中非零系数数受数据集中程度的控制。如果所涉功能是石英意义上的约美元 > 0美元的利普$(\伽玛),我们为GRIM获得了更好的趋同性能。特别是,我们证明,为确保GRIM发现经常参数$\伽玛 > 0美元方面的数据集中程度正在下降。