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Computationally Efficient Decompositions of Oblique Projection Matrices

Journal Article · · SIAM Journal on Matrix Analysis and Applications
DOI:https://doi.org/10.1137/19m1288115· OSTI ID:1680061
 [1];  [2];  [3]
  1. Argonne National Lab. (ANL), Lemont, IL (United States)
  2. Univ. of California, Merced, CA (United States)
  3. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
+ Show Author Affiliations
Oblique projection matrices arise in problems in weighted least squares, signal processing, and optimization. While these matrices can be potentially very large, their low-rank structure can be exploited for efficient computation. Here, we propose fast and scalable algorithms for computing their eigendecomposition and singular value decomposition (SVD). Numerical experiments that compare our proposed approaches to existing methods, including randomized SVD, are presented. In addition, we test their accuracy on linear systems from equality constrained optimization problems.
Research Organization:
Argonne National Laboratory (ANL), Argonne, IL (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
Sponsoring Organization:
National Science Foundation (NSF); USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
Grant/Contract Number:
AC02-06CH11357; AC52-07NA27344
OSTI ID:
1680061
Alternate ID(s):
OSTI ID: 1804290
Report Number(s):
LLNL-JRNL--817763; 162611
Journal Information:
SIAM Journal on Matrix Analysis and Applications, Journal Name: SIAM Journal on Matrix Analysis and Applications Journal Issue: 2 Vol. 41; ISSN 0895-4798
Publisher:
Society for Industrial and Applied Mathematics (SIAM)Copyright Statement
Country of Publication:
United States
Language:
English

References (10)

Representations of quasi-Newton matrices and their use in limited memory methods journal January 1994
Large-scale quasi-Newton trust-region methods with low-dimensional linear equality constraints journal September 2019
On scaled projections and pseudoinverses journal January 1989
On bounds for scaled projections and pseudoinverses journal April 1990
Signal processing applications of oblique projection operators journal June 1994
An Analysis of the Total Least Squares Problem journal December 1980
Finding Structure with Randomness: Probabilistic Algorithms for Constructing Approximate Matrix Decompositions journal January 2011
Quasi-Newton Methods, Motivation and Theory journal January 1977
Block-Iterative Algorithms with Diagonally Scaled Oblique Projections for the Linear Feasibility Problem journal January 2002
CUTEr and SifDec: A constrained and unconstrained testing environment, revisited journal December 2003

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Related Subjects

97 MATHEMATICS AND COMPUTING
SVD
eigendecomposition
oblique projection matrices
projections
randomized singular value decomposition
singular value decomposition