Related papers: Algorithms for structured matrix-vector product of…
In this paper we deal with the connection of frames with the class of Hilbert Schmidt operators. First we give an easy criteria for operators being in this class using frames. It is the equivalent to the criteria using orthonormal bases.…
The computation of the structured pseudospectral abscissa and radius (with respect to the Frobenius norm) of a Toeplitz matrix is discussed and two algorithms based on a low rank property to construct extremal perturbations are presented.…
The multiplication of matrices is an important arithmetic operation in computational mathematics. In the context of hierarchical matrices, this operation can be realized by the multiplication of structured block-wise low-rank matrices,…
We show that every n-by-n matrix is generically a product of [n/2] + 1 Toeplitz matrices and always a product of at most 2n+5 Toeplitz matrices. The same result holds true if the word "Toeplitz" is replaced by "Hankel", and the generic…
By a tensor we mean an element of a tensor product of vector spaces over a field. Up to a choice of bases in factors of tensor products, every tensor may be coordinatized, that is, represented as an array consisting of numbers. This note is…
We present here new mechanisms for hashing data via binary embeddings. Contrary to most of the techniques presented before, the embedding matrix of our mechanism is highly structured. That enables us to perform hashing more efficiently and…
Matrix-valued optimization tasks, including those involving symmetric positive definite (SPD) matrices, arise in a wide range of applications in machine learning, data science and statistics. Classically, such problems are solved via…
Matrix--vector algorithms, particularly Krylov subspace methods, are widely viewed as the most effective algorithms for solving large systems of linear equations. This paper establishes lower bounds on the worst-case number of…
We study linear problems defined on tensor products of Hilbert spaces with an additional (anti-) symmetry property. We construct a linear algorithm that uses finitely many continuous linear functionals and show an explicit formula for its…
This paper considers the problem of robustly estimating a structured covariance matrix with an elliptical underlying distribution with known mean. In applications where the covariance matrix naturally possesses a certain structure, taking…
Recursive blocked algorithms have proven to be highly efficient at the numerical solution of the Sylvester matrix equation and its generalizations. In this work, we show that these algorithms extend in a seamless fashion to…
We consider the famous Strassen algorithm for fast multiplication of matrices. We show that this algorithm has a nontrivial finite group of automorphisms of order 36 (namely the direct product of two copies of the symmetric group on 3…
Rank deficient Hankel matrices are at the core of several applications. However, in practice, the coefficients of these matrices are noisy due to e.g. measurements errors and computational errors, so generically the involved matrices are…
A cumbersome operation in numerical analysis and linear algebra, optimization, machine learning and engineering algorithms; is inverting large full-rank matrices which appears in various processes and applications. This has both numerical…
We consider an efficient computational framework for speeding up several machine learning algorithms with almost no loss of accuracy. The proposed framework relies on projections via structured matrices that we call Structured Spinners,…
In this rather brief note we present and discuss techniques for solving Kronecker matrix product least squares problems. Our main contribution is an iterative approach that uses the efficient Kronecker matrix-vector multiplication strategy…
The goal of this article is to study algorithms that compute the product between two matrixes, specifically using the ingenuous methods of Strassen and Strassen-Winograd, which will be presented in Section 2. At present, the cited methods…
Recent theory of mapping an image into a structured low-rank Toeplitz or Hankel matrix has become an effective method to restore images. In this paper, we introduce a generalized structured low-rank algorithm to recover images from their…
Automated model selection is an important application in science and engineering. In this work, we develop a learning approach for identifying structured dynamical systems from undersampled and noisy spatiotemporal data. The learning is…
The subject of Chapter 1 is GKK $\tau$-matrices and related topics. Chapter 2 is devoted to boundedly invertible collections of matrices, with applications to operator norms and spline approximation. Various structured matrices (Toeplitz,…