The content discusses the discretization of non-local operators leading to large matrices and the use of H2-matrices for data-sparse approximation. It introduces an algorithm for multiplying H2-matrices with error control and explains the hierarchical structure involved in matrix operations.
H2-matrices exploit local low-rank structures in large matrices to reduce storage requirements and complexity. The article details algorithms for constructing efficient preconditioners and evaluating matrix functions using H2-matrices.
Specialized techniques like fast multipole methods are employed to handle dense matrices efficiently in integral equations. The text delves into the complexities of matrix multiplication, especially when approximating products of H2-matrices within a block structure.
The concept of cluster trees and block trees is crucial in representing submatrices efficiently during matrix operations. The discussion extends to semi-uniform matrices, accumulators, induced block structures, basis trees, and their yields in optimizing matrix computations.
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by Stef... alle arxiv.org 03-05-2024
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