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Organizing Committee
Tel Aviv University
Purdue University
University of California Irvine
Virginia Tech
North Carolina State University
Università di Bologna
Abstract
This workshop will highlight the latest advances and emerging trends in the area of randomized numerical linear algebra (RandNLA). RandNLA uses randomization to reduce communication and computation costs in low-rank approximations, optimization, preconditioning, and other areas across Scientific Computing and Data Science. Key topics of interest to this workshop include sketching, sampling, stochastic rounding, and mixed precision computations to improve efficiency in linear and multilinear algebra, optimization, inverse problems and uncertainty quantification. We also aim to bring in new perspectives from high-dimensional probability and random matrix theory. By bringing together researchers from numerical analysis, theoretical computer science, and related fields, the workshop aims to bridge theory, practice, and applications.
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Workshop Schedule
Monday, February 02, 2026
10:00 - 10:20 AM EST
Check In & Coffee Break
Check In - 11th Floor Collaborative Space
10:20 - 10:30 AM EST
Welcome
11th Floor Lecture Hall
Brendan Hassett, ICERM/Brown University
10:30 - 11:15 AM EST
Randomized Mixed-Precision Solution of Least Squares Problems
11th Floor Lecture Hall
Speaker
Ilse Ipsen, North Carolina State University
Session Chair
Arvind Krishna Saibaba, North Carolina State University
Abstract
We consider the solution of full column-rank least squares problems by means of normal equations that are preconditioned, symmetrically or non symmetrically, with a randomized preconditioner that is computed in lower arithmetic precision. With an effective preconditioner, the solutions from the preconditioned normal equations are almost as accurate as those from the QR-based Matlab backslash (mldivide) command -- even for highly illconditioned matrices. This means the accuracy of the preconditioned normal equations depends on the residual of the original least squares problem, but does not depend on the accuracy of the preconditioner. We present realistic perturbation bounds for the relative error in the computed solutions. This is joint work with James Garrison.
11:30 AM - 12:15 PM EST
CUR approximation: computation and applications
11th Floor Lecture Hall
Speaker
Yuji Nakatsukasa, University of Oxford
Session Chair
Arvind Krishna Saibaba, North Carolina State University
Abstract
The CUR approximation of a matrix is appealing because, once the column and row indices are selected, it yields a low-rank approximation without even looking at the whole matrix. Remarkably, for any matrix there exists a CUR approximation that is near-best when compared with the truncated SVD. Efficient algorithms for computing CUR approximations have been developed, making them a competitive alternative in large-scale computations. In this talk, I will first discuss the computational and theoretical aspects of CUR, then highlight its power in practical applications, including approximation theory, model reduction and the solution of parameter-dependent problems.
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 3:15 PM EST
Recent Developments in RandNLA: Random Matrix Theory for Modern Machine Learning?
11th Floor Lecture Hall
Speaker
Michael Mahoney, University of California, Berkeley
Session Chair
Valeria Simoncini, Università di Bologna
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 4:20 PM EST
On tensor-structured linear measurements: trimming and efficient low-rank recovery
11th Floor Lecture Hall
Speaker
Elizaveta Rebrova, Princeton
Session Chair
Valeria Simoncini, Università di Bologna
Abstract
Data-oblivious measurements play an important role in low-rank data compression and recovery techniques, frequently used in streaming settings and within iterative algorithms. When data is tensorial, a special challenge is to create a sketch with a structure that reflects tensor structure: this way, it can work similarly to a dense unstructured random matrix but can be applied faster and stored much more efficiently. Theoretical guarantees for many standard iterative low-rank recovery methods are based on assumptions on the measurement operator, such as restricted isometry properties (RIP). However, tensor-structured random linear maps often lack good restricted isometry behavior; in particular, they do not preserve the norms of low-rank tensors sufficiently well for standard analyses. I discuss several ways that we recently proposed to address this, including local trimming techniques that provably restore pointwise geometry-preservation properties of tensor-structured maps, making them comparable to those of unstructured sub-Gaussian measurements.
4:30 - 4:50 PM EST
Capacity Analysis of Vector Symbolic Architectures
11th Floor Lecture Hall
Speaker
Shashanka Ubaru, IBM Research & Oden Institute, UT Austin
Session Chair
Valeria Simoncini, Università di Bologna
Abstract
Hyperdimensional computing (HDC) is a biologically inspired framework which represents symbols with high-dimensional vectors and uses vector operations to manipulate them. The ensemble of a particular vector space and a prescribed set of vector operations (including one addition-like for "bundling" and one outer-product-like for "binding") form a vector symbolic architecture (VSA). While VSAs have been employed in numerous applications and have been studied empirically, many theoretical questions about VSAs remain open. We analyze the representation capacities of four common VSAs: MAP-I, MAP-B, and two VSAs based on sparse binary vectors. "Representation capacity' here refers to bounds on the dimensions of the VSA vectors required to perform certain symbolic tasks, such as testing for set membership and estimating set intersection sizes for two sets of symbols to a given degree of accuracy. We also analyze the ability of a novel variant of a Hopfield network (a simple model of associative memory) to perform some of the same tasks that are typically asked of VSAs. In addition to providing new bounds on VSA capacities, our analyses establish and leverage connections between VSAs, "sketching" (dimensionality reduction) algorithms, and Bloom filters.
5:00 - 6:30 PM EST
Reception
11th Floor Collaborative Space
Tuesday, February 03, 2026
9:00 - 9:45 AM EST
Fast randomized algorithms for structured matrices
11th Floor Lecture Hall
Speaker
Per-Gunnar Martinsson, University of Texas at Austin
Session Chair
Anna Ma, University of California Irvine
Abstract
The talk describes a set of recently developed randomized algorithms for computing a data sparse representation of a rank structured matrix (such as an H-matrix, or an HSS matrix). The algorithms are black box in the sense that they interact with the matrix to be compressed only through its action on vectors, making them ideal for tasks such as forming Schur complements or matrix matrix multiplication. In situations where the operator to be compressed (and its transpose) can be applied in O(N) operations, the compression as a whole has linear complexity as well, in many environments. Of particular interest is a recent technique that simultaneously both compresses and factorizes an H-matrix with a strong admissibility criterion.
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
Randomized Householder-Cholesky QR Factorization with Multisketching
11th Floor Lecture Hall
Speaker
Daniel Szyld, Temple University
Session Chair
Anna Ma, University of California Irvine
Abstract
We present and analyze a new randomized algorithm called rand-cholQR
for computing tall-and-skinny QR factorizations. Using one or two random sketch matrices, it is proved that with high probability, its orthogonality error is bounded by a constant of the order of unit roundoff for any numerically full-rank matrix. An evaluation of the performance of rand-cholQR on a NVIDIA A100 GPU demonstrates that for tall-and-skinny matrices, rand-cholQR with multiple sketch matrices is nearly as fast as, or in some cases faster than, the state-of-the-art CholeskyQR2. Hence, compared to CholeskyQR2, rand-cholQR is more stable with almost no extra computational or memory cost, and therefore a superior algorithm both in theory and practice. (Joint work with Andrew Higgins, Erik Boman, and Ichitaro Yamazaki)
11:30 AM - 12:15 PM EST
Streaming randomized techniques for low-rank approximation of tensors with applications
11th Floor Lecture Hall
Speaker
Alberto Bucci, University of Edinburgh
Session Chair
Vishwas Rao, Argonne National Laboratory
Abstract
Randomized and streaming techniques have become standard tools for constructing low-rank approximations of large-scale matrices, offering single-pass algorithms with strong computational and memory advantages. In this talk, we first recall the basic principles underlying randomized matrix approximation, highlighting their strengths and limitations in a streaming setting. We then extend these ideas to higher-order tensors and review how randomized streaming techniques can be formulated in several tensor formats, including the Tucker and tensor-train decompositions. Building on this perspective, we discuss how the same principles naturally generalize to more complex structures such as tree tensor networks. The second part of the talk focuses on tensor-train representations and their integration into iterative linear solvers. In particular, we show how streaming randomized approximations can be embedded into Krylov subspace methods such as sketched GMRES, leading to efficient tensor-structured solvers that avoid expensive intermediate tensor contractions. While we focus on the tensor-train format, the proposed framework is sufficiently general to be applied to other tensor network architectures.
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 3:15 PM EST
Fast Construction of Hierarchically Low-Rank Matrices Using Randomized Sketching
11th Floor Lecture Hall
Speaker
Xiaoye Li, Lawrence Berkeley National Laboratory
Session Chair
Vishwas Rao, Argonne National Laboratory
Abstract
Hierarchically low-rank (H-LR) matrices have been widely used to design fast solvers solvers for integral equations, boundary element methods, discretized PDEs, and kernel matrices in statistical and machine learning. These matrices include H/H2-matrices, HODLR matrices, HSS matrices and butterfly matrices. They differ in the treatment of the off-diagonal low-rank structures. These matrices can be used in iterative solvers where stuctured-matrix-vector-product is needed, or in direct solvers where structured-factorization and stuctured-solve are needed. The computational bottleneck in these types of solvers is often the construction algorithm which converts a standard dense matrix into an H-LR format. The dense matrix may not be explicitly stored. In recent advances of this field, we have seen extensive use of randomized sketching to speed up the construction process. Regardless of which H-LR formats, the common questions include:
1) which random matrix to use?
2) what size of the random matrix to use?
3) what are the error bounds of the H-LR approximation?
4) what are the key ingredients needed for high performance implementations?
We will present a unified view to answer these questions, illustrate
the algorithms on various applications, and discuss some open problems."
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 5:00 PM EST
Wednesday, February 04, 2026
9:00 - 9:45 AM EST
Subspace injections
11th Floor Lecture Hall
Speaker
Joel Tropp, California Institute of Technology
Session Chair
Harbir Antil, George Mason University
Abstract
To achieve the greatest possible speed, practitioners regularly implement randomized algorithms for low-rank approximation and least-squares regression with structured dimension reduction maps. This talk outlines a new perspective on structured dimension reduction, based on the injectivity properties of the dimension reduction map. This approach provides sharper bounds for sparse dimension reduction maps, and it leads to exponential improvements for tensor-product dimension reduction. Empirical evidence confirms that these types of structured random matrices offer exemplary performance for a range of synthetic problems and contemporary scientific applications.
Joint work with Chris Camaño, Ethan Epperly, and Raphael Meyer. Available at arXiv:2508.21189.
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
Randomized methods for joint eigenvalue problems
11th Floor Lecture Hall
Speaker
Daniel Kressner, École Polytechnique Fédérale de Lausanne
Session Chair
Harbir Antil, George Mason University
Abstract
Joint eigenvalue problems are, broadly speaking, concerned with computing common eigenvectors and the corresponding eigenvalues for families of matrices. In this talk, we will survey the development and analysis of randomized methods for solving such joint eigenvalue problems. Several applications related to signal processing and multivariate root finding will be illustrated. This talk is based on joint work with Haoze He and Bor Plestenjak.
11:30 AM - 12:15 PM EST
Matrix-Mimetic Tensor Algebra: Optimal Decompositions and Equivariant Learning
11th Floor Lecture Hall
Speaker
Lior Horesh, IBM Research
Session Chair
Harbir Antil, George Mason University
Abstract
High-dimensional information often contains complex multi-dimensional correlations that traditional matrix-based algorithms often fail to capture. While numerous tensor algebra frameworks have been proposed over the years, each lacked critical properties inherent to matrix algebra. The novel tensor-tensor algebra formalism preserves these matrix-mimetic properties while simultaneously resolving a decades-long open problem in tensor analysis: providing an Eckart-Young-like representation theorem for tensors. This framework delivers provably optimal, yet computationally feasible, algorithm for revealing intricate high-dimensional correlations through tensor decompositions. The mimetic properties of the tensor-tensor formalism enable seamless retrofitting of existing computational workflows into tensorial ones. We demonstrate this by tensorizing specialized neural network structures and extending the framework to dynamic graphs through tensor Graph Convolutional Neural Networks, achieving effective representation learning for time-evolving structures. We conclude by exploring recent developments in tensor group symmetry theory, which generalize the algebraic framework to equivariant domains.
12:25 - 12:30 PM EST
Group Photo (Immediately After Talk)
11th Floor Lecture Hall
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 3:15 PM EST
Fairness, Sampling, and Federated Settings in Iterative Learning
11th Floor Lecture Hall
Speaker
Deanna Needell, UCLA
Session Chair
Petros Drineas, Purdue University
Abstract
In this talk, we will discuss several areas of recent work centered around the themes of fairness and foundations in machine learning as well as highlight the challenges in this area. We will discuss recent results involving linear algebraic tools for learning, such as methods in non-negative matrix factorization that include tailored approaches for fairness. Then, we will discuss new foundational results that theoretically justify phenomena like benign overfitting in neural networks. Lastly, we will mention some recent results on observational multiplicity, and how those can be utilized to improve equity. Throughout the talk, we will include example applications from collaborations with community partners, using machine learning to help organizations with fairness and justice goals. This talk includes work joint with Erin George, Kedar Karhadkar, Lara Kassab, and Guido Montufar.
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 4:20 PM EST
The S^T S-SVD with Applications
11th Floor Lecture Hall
Speaker
Davide Palitta, Alma Mater Studiorum, Universita' di Bologna
Session Chair
Petros Drineas, Purdue University
Abstract
Sketching techniques have gained popularity in numerical linear algebra to accelerate the solution of least squares problems. The so-called ε-subspace embedding property of a sketching matrix has been largely used to characterize the problem residual norm, since the procedure is no longer optimal in terms of the (classical) Frobenius or Euclidean norm. By building on available results on the SVD of the sketched matrix SA derived by Gilbert, Park, and Wakin (Proc. of SPARS-2013), a novel decomposition of A itself, the S^T S-SVD, is proposed, which is exact with high probability, and in which the left singular vectors are orthonormal with respect to a (semi-)norm defined by the sketching matrix S. The new decomposition is less expensive to compute, while preserving the singular values with probabilistic confidence. In addition to present this new decomposition, in this talk we will show how the S^T S-SVD is the right tool to analyze the quality of several sketching techniques in the literature, for which examples are reported. For instance, it is possible to simply bound the distance from (standard) orthogonality of sketched orthogonal matrices in state-of-the-art randomized QR algorithms. If time allows, as a further application, the classical problem of the nearest orthogonal matrix will be generalized to the new S^T S-orthogonality, and the S^T S-SVD will be adopted to solve it.
This talk is based on a joint work with Valeria Simoncini.
4:30 - 4:50 PM EST
Structured Matrix Learning from Matrix-Vector Products
11th Floor Lecture Hall
Speaker
Chris Musco, New York University
Session Chair
Petros Drineas, Purdue University
Abstract
I will discuss the problem of approximating an arbitrary target matrix A with a structured matrix, given access to just a limited number of adaptively chosen matrix-vector products with A. This general problem is ubiquitous in computational science, both in algorithmic applications and, more recently, in Scientific Machine Learning (SciML), where it abstracts the central task of operator learning.
For common structures, like low-rank matrices, the number of matrix-vector products required to obtain a near-optimal approximation to A is well understood. Indeed, optimal results are obtained by the randomized singular value decomposition (RandSVD) and related methods. However, for a number of other important structures, like sparse or hierarchically structured matrices, results have been more elusive. I will present recent work that makes progress on matvec-efficient algorithms for these structured classes and others. I will also discuss my group's work on trying to develop a general theory for the complexity of structured matrix learning.
This talk presents joint work with Noah Amsel, Pratyush Avi, Tyler Chen, Prathamesh Dharangutte, Chinmay Hegde, Feyza Duman Keles, Diana Halikias, Cameron Musco, and David Persson.
Thursday, February 05, 2026
9:00 - 9:45 AM EST
Importance Sampling for Nonlinear Models
11th Floor Lecture Hall
Speaker
Fred Roosta, University of Queensland
Session Chair
Julianne Chung, Emory University
Abstract
While norm-based and leverage-score-based methods have been extensively studied for identifying "important" data points in linear models, analogous tools for nonlinear models remain significantly underdeveloped. By introducing the concept of the adjoint operator of a nonlinear map, we address this gap and generalize norm-based and leverage-score-based importance sampling to nonlinear settings. We demonstrate that sampling based on these generalized notions of norm and leverage scores provides approximation guarantees for the underlying nonlinear mapping, similar to linear subspace embeddings. As direct applications, these nonlinear scores not only reduce the computational complexity of training nonlinear models by enabling efficient sampling over large datasets but also offer a novel mechanism for model explainability and outlier detection. Our contributions are supported by both theoretical analyses and experimental results across a variety of supervised learning scenarios.
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
Estimating a matrix's singular values with interpolative decompositions
11th Floor Lecture Hall
Speaker
Alex Townsend, Cornell University
Session Chair
Julianne Chung, Emory University
Abstract
Randomized linear algebra has shown that many matrix approximation tasks can be solved efficiently by sampling and sketching, yet deterministic rank revealing methods remain a central step. In this talk, we examine recent theoretical results that clarify what greedy pivoting can and cannot guarantee in rank-revealing factorizations. We first describe a local maximum-volume perspective on pivoted Gaussian elimination and QR factorizations, which yields sharp conditions for when deterministic pivoting reliably reveals numerical rank. We then contrast this with pivoted Cholesky factorizations applied to matrices arising from smooth kernels, showing that greedy pivoting cannot exhibit Kahan-like behavior.
11:30 - 11:50 AM EST
Closing the Theory-Practice Gap in Oblivious Subspace Embeddings
11th Floor Lecture Hall
Speaker
Michal Dereziński, University of Michigan
Session Chair
Swati Padmanabhan, University of Minnesota Twin Cities
Abstract
A subspace embedding is a random linear transformation that maps high-dimensional vectors to a lower dimension that with high probability preserves the norms of all vectors in a low-dimensional subspace up to a small relative error. Due to their simplicity and computational efficiency, subspace embeddings have been the central dimensionality reduction technique in numerical linear algebra problems such as least squares regression and low-rank approximation for the past two decades. Yet, despite their popularity, there remains a fundamental theory-practice gap in our understanding of subspace embeddings, which is characterized by a conjecture of Nelson and Nguyen (FOCS 2013) about the optimal embedding dimension that can be attained efficiently. In this talk, I will discuss recent efforts in closing this theory-practice gap by analyzing the universality properties of sparse random matrices, which has led to resolving the conjecture up to sub-polylogarithmic factors (SODA 2026). Based on joint works with Shabarish Chenakkod, Xiaoyu Dong, and Mark Rudelson.
12:00 - 12:20 PM EST
Preconditioning without a preconditioner using block Krylov subspace methods
11th Floor Lecture Hall
Speaker
Tyler Chen, JPMorganChase
Session Chair
Swati Padmanabhan, University of Minnesota Twin Cities
Abstract
We describe a randomized variant of the block conjugate gradient method for solving a single positive-definite linear system of equations. Our method provably outperforms preconditioned conjugate gradient with a broad-class of Nyström- based preconditioners, without ever explicitly constructing a preconditioner. In analyzing our algorithm, we derive theoretical guarantees for new variants of Nyström preconditioned conjugate gradient which may be of separate interest. We also describe how our approach yields state-of-the-art algorithms for key data-science tasks such as computing the entire ridge regression regularization path and generating multiple independent samples from a high-dimensional Gaussian distribution.
12:30 - 2:30 PM EST
Lunch/Free Time
2:30 - 2:50 PM EST
An adaptive randomized pivoting strategy for low-rank approximation
11th Floor Lecture Hall
Speaker
Alice Cortinovis, University of Pisa
Session Chair
Swati Padmanabhan, University of Minnesota Twin Cities
Abstract
We consider the column subset selection problem, that is, the problem of selecting a few representative columns of a matrix in order to construct a good low-rank approximation. We present a randomized algorithm, based on an adaptive leverage score sampling strategy, which guarantees, in expectation, an approximation error that matches the optimal existence result in the Frobenius norm. Our method, called Adaptive Randomized Pivoting (ARP), can be seen as a randomized counterpart to a recent deterministic approach proposed by Osinsky. Although the same theoretical guarantee can be achieved with other methods, such as volume sampling, ARP is simpler and less expensive. We will highlight how this simple yet powerful strategy can be adapted to a range of other tasks related to low-rank approximation, including the Discrete Empirical Interpolation Method, cross/skeleton approximation, and the Nyström approximation of positive semidefinite matrices.
3:00 - 3:20 PM EST
Everything is Vecchia: Unifying low-rank and sparse inverse approximations
11th Floor Lecture Hall
Speaker
Robert Webber, UC San Diego
Session Chair
Swati Padmanabhan, University of Minnesota Twin Cities
Abstract
The partial pivoted Cholesky approximation accurately represents matrices that are close to being low-rank. Meanwhile, the Vecchia approximation accurately represents matrices with inverse Cholesky factors that are close to sparse. What happens if a partial Cholesky approximation is combined with a Vecchia approximation of the residual? The sum can be rewritten as a Vecchia approximation of the original matrix with an amplified sparsity pattern. Thus, the Vecchia approximation is a superset for other factored matrix approximations and it has broad applicability.
3:30 - 4:00 PM EST
Coffee Break
11th Floor Collaborative Space
4:00 - 5:00 PM EST
Friday, February 06, 2026
9:00 - 9:45 AM EST
Tight Sampling Bounds for Eigenvalue Approximation
11th Floor Lecture Hall
Speaker
David Woodruff, Carnegie Mellon University
Session Chair
Haim Avron, Tel Aviv University
Abstract
Estimating the spectrum of a matrix is a fundamental problem in numerical linear algebra. In this talk, we explore the efficiency of estimating the spectrum of a symmetric matrix with bounded entries using entrywise sampling. Prior work established that an eps * n additive approximation to all eigenvalues could be achieved by sampling a principal submatrix of size poly(log n) / eps^3. We show that a sample size of O~(1/eps^2) is sufficient, removing the dependence on n and obtaining optimal dependence on eps up to log(1/eps) factors.
We extend these techniques to achieve tight bounds for related problems. We show that an eps * ||A||_F additive approximation via squared row-norm sampling requires only O~(1/eps^2) samples, improving the previous O~(1/eps^8) bound. Furthermore, for bounded entry PSD matrices, we prove that sampling O(1/eps) columns allows for a non-adaptive approximation of the top eigenvector to within eps * n additive error. Finally, we discuss applications of these results, including faster eigenvalue estimation sketches for dense matrices and improved sample complexity for approximating the spectrum of bounded entry PSD matrices.
Based on joint work with William Swartworth
10:00 - 10:30 AM EST
Coffee Break
11th Floor Collaborative Space
10:30 - 11:15 AM EST
The Polar Express: Optimal Matrix Sign Methods and Their Application to the Muon Algorithm
11th Floor Lecture Hall
Speaker
Robert Gower, Flatiron Institute
Session Chair
Haim Avron, Tel Aviv University
Abstract
Computing the polar decomposition and the related matrix sign function has been a well-studied problem in numerical analysis for decades. Recently, it has emerged as an important subroutine within the Muon algorithm for training deep neural networks. However, the requirements of this application differ sharply from classical settings: deep learning demands GPU-friendly algorithms that prioritize high throughput over high precision. We introduce Polar Express, a new method for computing the polar decomposition. Like Newton-Schulz and other classical polynomial methods, our approach uses only matrix-matrix multiplications, making it very efficient on GPUs. Inspired by earlier work of Chen & Chow and Nakatsukasa & Freund, Polar Express adapts the update rule at each iteration by solving a minimax optimization problem. We prove that this strategy minimizes error in a worst-case sense, allowing Polar Express to converge as rapidly as possible both in the early iterations and asymptotically. We also address finite-precision issues, making it practical to use in bfloat16. When integrated into the Muon training framework, our method leads to consistent improvements in validation loss when training a GPT-2 model on one billion tokens from the FineWeb dataset, outperforming recent alternatives across a range of learning rates.
11:30 AM - 12:15 PM EST
Structured Matrix Approximations via Tensor Decompositions
11th Floor Lecture Hall
Speaker
Misha Kilmer, Tufts University
Session Chair
Haim Avron, Tel Aviv University
Abstract
We provide a computational framework for approximating a class of structured matrices; here, the term structure is very general. Our matrix-to-tensor invertible mapping allows us to pose the matrix-approximation problem as a tensor-approximation problem. Mapping the tensor approximant back to matrix space, we obtain a structured matrix approximation that can be expressed as a sum of structured Kronecker products, or in block low-rank form, or as a sum of mixed Kronecker and block structured matrices, depending on which tensor decomposition is employed. We illustrate the ability of our method to uncover latent structure in the operators that can be leveraged in large-scale computations and consider where our approach could benefit from randomization. This is joint work with Arvind Saibaba (NCSU).
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