We conducted an extensive computational experiment, lasting multiple
CPU-years, to optimally select parameters for two important classes of
algorithms for finding sparse solutions of underdetermined systems of linear
equations. We make the optimally tuned implementations available at {\tt
sparselab.stanford.edu}; they run `out of the box' with no user tuning: it is
not necessary to select thresholds or know the likely degree of sparsity. Our
class of algorithms includes iterative hard and soft thresholding with or
without relaxation, as well as CoSaMP, subspace pursuit and some natural
extensions. As a result, our optimally tuned algorithms dominate such
proposals. Our notion of optimality is defined in terms of phase transitions,
i.e. we maximize the number of nonzeros at which the algorithm can successfully
operate. We show that the phase transition is a well-defined quantity with our
suite of random underdetermined linear systems. Our tuning gives the highest
transition possible within each class of algorithms.

本研究中，我们对寻找欠定线性方程组的稀疏解的两个重要算法进行了广泛的计算实验，并进行了最优参数选择。我们的优化程序在 sparselab.stanford.edu 上提供，并且在没有用户调整的情况下运行 “开箱即用”。我们通过我们的随机欠定线性系统套件，使用相变的概念对我们的算法进行了最优化，并展示了我们调整程序使每类算法内达到了可能的最高相变。