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Block-adaptive Cross Approximation of Discrete Integral Operators

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M. Bauer, M. Bebendorf

Numerical Analysis · Submitted 6 May 2019

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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arXiv ID1905.01918 (version 1)
Pith ID64HL2OUH, Pith's permanent record of this paper and its review
CitationM. Bauer, M. Bebendorf. "Block-adaptive Cross Approximation of Discrete Integral Operators." arXiv:1905.01918 (2019). https://pith.science/paper/64HL2OUH
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,625 input tokens.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.09 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.70 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; .

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 block-wise matrix approximation. This allows to interlace the assembling of the coefficient matrix with the iterative solution.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 1.00 0.89 0.18 asserted 1.00
s1 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. background 0.71 0.11 0.13 hedged possibility 1.00
s2 To this end, error estimation techniques known from adaptive mesh refinement are applied to automatically improve the block-wise matrix approximation. method 0.96 0.41 0.09 asserted 0.98
s3 This allows to interlace the assembling of the coefficient matrix with the iterative solution. interpretation 0.36 0.57 0.13 asserted 0.94

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from argument 0.75.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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 block-wise matrix approximation. This allows to interlace the assembling of the coefficient matrix with the iterative solution.

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