The objective of this work is single image super-resolution (SR), in which the input is specified by a low-resolution image and a consistent higher-resolution image should be returned. We propose a novel post-processing procedure named iterative fine-tuning and approximation (IFA) for mainstream SR methods. Internal image statistics are complemented by iteratively fine-tuning and performing linear subspace approximation on the outputs of existing external SR methods, helping to better reconstruct missing details and reduce unwanted artifacts. The primary concept of our method is that it first explores and enhances internal image information by grouping similar image patches and then finds their sparse or low-rank representations by iteratively learning the bases or primary components, thereby enhancing the primary structures and some details of the image. We evaluate the proposed IFA procedure over two standard benchmark datasets and demonstrate that IFA can yield substantial improvements for most existing methods via tweaking their outputs, achieving state-of-the-art performance.