On computing sparse generalized inverses

被引：0

作者：

Ponte, Gabriel ^{[1
,2
]}

Fampa, Marcia ^{[2
]}

Lee, Jon ^{[1
]}

Xu, Luze ^{[3
]}

机构：

[1] Univ Michigan, Ann Arbor, MI 48109 USA

[2] Univ Fed Rio de Janeiro, Rio De Janeiro, Brazil

[3] Univ Calif Davis, Davis, CA USA

来源：

OPERATIONS RESEARCH LETTERS | 2024年 / 52卷

基金：

美国国家科学基金会;

关键词：

Moore-Penrose pseudoinverse; Generalized inverse; Sparse optimization; Norm minimization; Least squares; Linear program;

D O I：

10.1016/j.orl.2023.107058

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

The M-P (Moore-Penrose) pseudoinverse is used in several linear-algebra applications. It is convenient to construct sparse block-structured matrices satisfying some relevant properties of the M-P pseudoinverse for specific applications. Aiming at row-sparse generalized inverses, we consider 2,1-norm minimization (and generalizations). We show that a 2,1-norm minimizing generalized inverse satisfies two additional M-P properties, including one needed for computing least-squares solutions. We present formulations related to finding row-sparse generalized inverses that can be solved very efficiently, which we verify numerically.(c) 2023 Elsevier B.V. All rights reserved.

引用

页数：6

共 16 条

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[3] Dokmanic I, 2017, Arxiv, DOI arXiv:1706.08349
[4] Dokmanic I, 2013, INT CONF ACOUST SPEE, P6526, DOI 10.1109/ICASSP.2013.6638923
[5] Dokmanic Ivan, 2017, Beyond Moore-Penrose Part II: the sparse pseudoinverse
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Lee, Jon
Ponte, Gabriel
Xu, Luze
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Fampa, Marcia
Lee, Jon
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[9] Fuentes V., 2016, CLAIO 2016, P343
[10] Golub G.H., 2013, Matrix computations, VFourth

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