Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the…
SIAM Journal on Matrix Analysis and Applications Template
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About the SIAM Journal on Matrix Analysis and Applications format
SIAM Journal on Matrix Analysis and Applications is a peer-reviewed journal published by SIAM, covering Matrix Theory and Algorithms, Advanced Optimization Algorithms Research, Electromagnetic Scattering and Analysis. Over its lifetime it has published 2,930 papers, which have received 132,901 citations.
| Publisher | SIAM |
|---|---|
| Reference style | Numbered (SIAM) Numbered — [1], [2] in the text [1] A. Smith, B. Jones, and C. Lee, A representative article title, SIAM Journal on Matrix Analysis and Applications 12 (2023) 45–58.
Formats any DOI in the closest standard style — SIAM Journal on Matrix Analysis and Applications has no published style definition, so this is an approximation. No sign-up. |
| Publishes research in | Matrix Theory and Algorithms Advanced Optimization Algorithms Research Electromagnetic Scattering and Analysis Numerical methods for differential equations Sparse and Compressive Sensing Techniques |
| ISSN | 0895-4798 |
| Citation impact (2-yr) | 2.97 |
| h-index | 151 |
| i10-index | 1,832 |
| Top institutions publishing here | Applied Mathematics (United States) |
| Journal website | www.siam.org |
| You get | A submission-ready PDF and the editable LaTeX source — ready to submit. |
Papers published in SIAM Journal on Matrix Analysis and Applications per year
Citation impact of SIAM Journal on Matrix Analysis and Applications by publication year
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Most-cited papers in SIAM Journal on Matrix Analysis and Applications
In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating…
In this paper, we analyze the main features and discuss the tuning of the algorithms for the direct solution of sparse linear systems on distributed memory computers developed in the context of a long term European research project. The algorithms use a multifrontal approach and are especially designed to cover a large class of problems.…
The problem of computing a small vertex separator in a graph arises in the context of computing a good ordering for the parallel factorization of sparse, symmetric matrices. An algebraic approach for computing vertex separators is considered in this paper. It is, shown that lower bounds on separator sizes can be obtained in terms of…
In this paper we discuss a multilinear generalization of the best rank-R approximation problem for matrices, namely, the approximation of a given higher-order tensor, in an optimal least-squares sense, by a tensor that has prespecified column rank value, row rank value, etc. For matrices, the solution is conceptually obtained by truncation of the singular value…