Abstract In this article, we extend the adaptive cross approximation (ACA) method known for the efficient approximation of discretisations of integral operators to a block-adaptive version. While ACA is usually employed to assemble hierarchical matrix approximations having the same prescribed accuracy on all blocks of the partition, for the solution of linear systems, it may be more efficient to adapt the accuracy of each block to the actual error of the solution as some blocks may be more important for the solution error than others. To this end, error estimation techniques known from adaptive mesh refinement are applied to automatically improve the blockwise matrix approximation. This allows to interlace the assembling of the coefficient matrix with the iterative solution.

中文翻译：

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离散积分算子的块自适应交叉逼近

摘要 在本文中，我们将已知的用于有效逼近积分算子离散化的自适应交叉逼近 (ACA) 方法扩展到块自适应版本。虽然 ACA 通常用于在分区的所有块上组装具有相同规定精度的分层矩阵近似，但对于线性系统的解决方案，使每个块的精度适应解决方案的实际误差可能更有效，因为某些块对于解决方案错误可能比其他块更重要。为此，从自适应网格细化已知的误差估计技术被应用以自动改进逐块矩阵近似。这允许将系数矩阵的组装与迭代解交错。