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We propose a new Iteratively Reweighted Least Squares (IRLS) algorithm for the problem of completing or denoising low-rank matrices that are structured, e.g., that possess a Hankel, Toeplitz or block-Hankel/Toeplitz structure. The algorithm…
We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors. Our algorithm, which we call TBMC (\emph{Tiling for Binary Matrix Completion}), gives interpretable output in the…
It is pointed out that separability problem for arbitrary multi-partite states can be fully solved by a finite size, elementary recursive algorithm. In the worse case scenario, the underlying numerical procedure, may grow doubly…
In this paper, we present a generalized Cuppen's divide-and-conquer algorithm for the symmetric tridiagonal eigenproblem. We extend the Cuppen's work to the rank two modifications of the form $A =T +\beta_1\bw_1\bw_1^T +…
This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…
Cylindrical Algebraic Decomposition (CAD) has long been one of the most important algorithms within Symbolic Computation, as a tool to perform quantifier elimination in first order logic over the reals. More recently it is finding…
The pivoted QLP decomposition is computed through two consecutive pivoted QR decompositions, and provides an approximation to the singular value decomposition. This work is concerned with a partial QLP decomposition of low-rank matrices…
Saddle point problems arise in many important practical applications. In this paper we propose and analyze some algorithms for solving symmetric saddle point problems which are based upon the block Gram-Schmidt method. In particular, we…
Software for computation of maximum likelihood estimates in linear structural equation models typically employs general techniques from non-linear optimization, such as quasi-Newton methods. In practice, careful tuning of initial values is…
We present a natural generalization of the recent low rank + sparse matrix decomposition and consider the decomposition of matrices into components of multiple scales. Such decomposition is well motivated in practice as data matrices often…
This paper deals with maximum entropy completion of partially specified block-circulant matrices. Since positive definite symmetric circulants happen to be covariance matrices of stationary periodic processes, in particular of stationary…
In recent research, the parallel performances of sweeping-type algorithms for high-frequency time-harmonic wave problems have been improved by departing from standard layer-type domain decomposition and introducing a new sweeping strategy…
This paper proposes a novel class of block quasi-Newton methods for convex optimization which we call symmetric rank-$k$ (SR-$k$) methods. Each iteration of SR-$k$ incorporates the curvature information with~$k$ Hessian-vector products…
We find an algorithmic procedure that enables to compute and to describe the structure of the isotropy subgroups of the group of complex orthogonal matrices with respect to the action of similarity on complex symmetric matrices. A key step…
In high-dimensional multivariate regression problems, enforcing low rank in the coefficient matrix offers effective dimension reduction, which greatly facilitates parameter estimation and model interpretation. However, commonly-used…
We propose a low-rank method for solving the Helmholtz equation. Our approach is based on the WaveHoltz method, which computes Helmholtz solutions by applying a time-domain filter to the solution of a related wave equation. The wave…
TriCG is a short-recurrence iterative method recently introduced by Montoison and Orban [SIAM J. Sci. Comput., 43 (2021), pp. A2502--A2525] for solving symmetric quasi-definite (SQD) linear systems. TriCG takes advantage of the inherent…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
When solving partial differential equations (PDEs) using finite difference or finite element methods, efficient solvers are required for handling large sparse linear systems. In this paper, a recursive sparse LU decomposition for matrices…
We give reconstruction algorithms for subclasses of depth-3 arithmetic circuits. In particular, we obtain the first efficient algorithm for finding tensor rank, and an optimal tensor decomposition as a sum of rank-one tensors, when given…