We make the interprecision transfers explicit in an algorithmic description of iterative refinement and obtain new insights into the algorithm. One example is the classic variant of iterative refinement where the matrix and the factorization are stored in a working precision and the residual is evaluated in a higher precision. In that case we make the observation that this algorithm will solve a promoted form of the original problem and thereby characterize the limiting behavior in a novel way and obtain a different version of the classic convergence analysis. We also discuss two approaches for interprecision transfer in the triangular solves.

翻译：我们在迭代求精法的算法描述中明确阐述了混合精度转换，并获得了对该算法的新见解。一个典型例子是经典的迭代求精变体，其中矩阵及其分解以工作精度存储，而残差则以更高精度计算。在这种情况下，我们观察到该算法将求解原始问题的提升形式，从而以新颖方式刻画其极限行为，并推导出经典收敛分析的不同版本。此外，我们还探讨了三角求解中混合精度转换的两种实现途径。