Robust Blockwise Random Pivoting: Fast and Accurate Adaptive Interpolative Decomposition

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Xuất bản năm:	arXiv.org (Dec 19, 2024), p. n/a
Tác giả chính:	Dong, Yijun
Tác giả khác:	Chen, Chao, Martinsson, Per-Gunnar, Pearce, Katherine
Được phát hành:	Cornell University Library, arXiv.org
Những chủ đề:	Parallel processing Tolerances Mathematical analysis Matrices (mathematics) Interpolation Optimization Approximation Algorithms Asymptotic properties Robustness (mathematics) Complexity Error detection Decomposition
Truy cập trực tuyến:	Citation/Abstract Full text outside of ProQuest
Các nhãn:	Thêm thẻ Không có thẻ, Là người đầu tiên thẻ bản ghi này!

Miêu tả
Bài tóm tắt:	The interpolative decomposition (ID) aims to construct a low-rank approximation formed by a basis consisting of row/column skeletons in the original matrix and a corresponding interpolation matrix. This work explores fast and accurate ID algorithms from comprehensive perspectives for empirical performance, including accuracy in both skeleton selection and interpolation matrix construction, efficiency in terms of asymptotic complexity and hardware efficiency, as well as rank adaptiveness. While many algorithms have been developed to optimize some of these aspects, practical ID algorithms proficient in all aspects remain absent. To fill in the gap, we introduce robust blockwise random pivoting (RBRP) that is asymptotically fast, hardware-efficient, and rank-adaptive, providing accurate skeletons and interpolation matrices comparable to the best existing ID algorithms in practice. Through extensive numerical experiments on various synthetic and natural datasets, we demonstrate the appealing empirical performance of RBRP from the aforementioned perspectives, as well as the robustness of RBRP to adversarial inputs.
số ISSN:	2331-8422
Nguồn:	Engineering Database