Bregman-type iterative methods have received considerable attention in recent years due to their ease of implementation and the high quality of the computed solutions they deliver. However, these iterative methods may require a large number of iterations and this reduces their usefulness. This paper develops a computationally attractive linearized Bregman algorithm by projecting the problem to be solved into an appropriately chosen low-dimensional Krylov subspace. The projection reduces the computational effort required for each iteration. A variant of this solution method, in which nonnegativity of each computed iterate is imposed, also is described. Extensive numerical examples illustrate the performance of the proposed methods.

布雷格曼型迭代方法由于易于实施且交付的计算解决方案质量高，近年来备受关注。但是，这些迭代方法可能需要大量的迭代，这降低了它们的实用性。本文通过投影要解决的问题为适当选择的低维Krylov子空间开发了一个计算上有吸引力的线性化布雷格曼算法。该投影减少了每次迭代所需的计算量。还描述了此解决方法的一种变体，其中对每个计​​算出的迭代项施加非负性。大量的数值示例说明了所提出方法的性能。