Related papers: Nearly Optimal Computations with Structured Matric…
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…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
Recovering low-rank and sparse matrices from incomplete or corrupted observations is an important problem in machine learning, statistics, bioinformatics, computer vision, as well as signal and image processing. In theory, this problem can…
This work was originally published by the author in 1999 in a book [1] and later became part of the author's doctoral thesis in 1999 [2]. Since the original language of these works is not English, the author provides a translation of the…
Homology features of spaces which appear in applications, for instance 3D meshes, are among the most important topological properties of these objects. Given a non-trivial cycle in a homology class, we consider the problem of computing a…
The standard way of solving the polynomial eigenvalue problem associated with a matrix polynomial is to embed the matrix polynomial into a matrix pencil, transforming the problem into an equivalent generalized eigenvalue problem. Such…
This paper investigates several cost-sparsity induced optimal input selection problems for structured systems. Given are an autonomous system and a prescribed set of input links, where each input link has a non-negative cost. The problems…
One matrix structure in the area of monotone Boolean functions is defined here. Some of its combinatorial, algebraic and algorithmic properties are derived. On the base of these properties, three algorithms are built. First of them…
Parallel matrix multiplication is one of the most studied fundamental problems in distributed and high performance computing. We obtain a new parallel algorithm that is based on Strassen's fast matrix multiplication and minimizes…
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,…
New algorithms are presented for computing annihilating polynomials of Toeplitz, Hankel, and more generally Toeplitz+ Hankel-like matrices over a field. Our approach follows works on Coppersmith's block Wiedemann method with structured…
We propose a general method for optimally approximating an arbitrary matrix $\mathbf{M}$ by a structured matrix $\mathbf{T}$ (circulant, Toeplitz/Hankel, etc.) and examine its use for estimating the spectra of genomic linkage disequilibrium…
We consider block-structured matrices $A_n$, where the blocks are of (block) unilevel Toeplitz type with $s\times t$ matrix-valued generating functions. Under mild assumptions on the size of the (rectangular) blocks, the asymptotic…
The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured $n\times n$ matrix it can be computed in $\mathcal{O}(n^3)$ operations. An interesting problem arises if the input…
The high computational cost involved in modeling of the progressive fracture simulations using large discrete lattice networks stems from the requirement to solve {\it a new large set of linear equations} every time a new lattice bond is…
Functions on a bounded domain in scientific computing are often approximated using piecewise polynomial approximations on meshes that adapt to the shape of the geometry. We study the problem of function approximation using splines on a…
Volker Strassen first suggested an algorithm to multiply matrices with worst case running time less than the conventional $\mathcal{O}(n^3)$ operations in 1969. He also presented a recursive algorithm with which to invert matrices, and…
For general large-scale optimization problems compact representations exist in which recursive quasi-Newton update formulas are represented as compact matrix factorizations. For problems in which the objective function contains additional…
By using the Hadamard matrix product concept, this paper introduces two generalized matrix formulation forms of numerical analogue of nonlinear differential operators. The SJT matrix-vector product approach is found to be a simple,…
Matrix orthogonal Laurent polynomials in the unit circle and the theory of Toda-like integrable systems are connected using the Gauss--Borel factorization of two, left and a right, Cantero-Morales-Velazquez block moment matrices, which are…