Related papers: Pixel Arrays: A fast and elementary method for sol…
Based on the matrix expression of general nonlinear numerical analogues presented by the present author, this paper proposes a novel philosophy of nonlinear computation and analysis. The nonlinear problems are considered an ill-posed linear…
We present an alternate formulation of the partial assignment problem as matching random clique complexes, that are higher-order analogues of random graphs, designed to provide a set of invariants that better detect higher-order structure.…
Recently the authors presented a matrix representation approach to real Appell polynomials essentially determined by a nilpotent matrix with natural number entries. It allows to consider a set of real Appell polynomials as solution of a…
The null vector method, based on a simple linear algebraic concept, is proposed as a solution to the phase retrieval problem. In the case with complex Gaussian random measurement matrices, a non-asymptotic error bound is derived, yielding…
We present a simple nearest-neighbor (NN) approach that synthesizes high-frequency photorealistic images from an "incomplete" signal such as a low-resolution image, a surface normal map, or edges. Current state-of-the-art deep generative…
We present a hierarchy of tractable relaxations to obtain lower bounds on the minimum value of a polynomial over a constraint set defined by polynomial equations. In contrast to previous convex relaxation techniques for this problem, our…
Nonlinear least-squares problems are a special class of unconstrained optimization problems in which their gradient and Hessian have special structures. In this paper, we exploit these structures and proposed a matrix-free algorithm with a…
Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
This paper presents a novel method designed to enhance the efficiency and accuracy of both image retrieval and pixel retrieval. Traditional diffusion methods struggle to propagate spatial information effectively in conventional graphs due…
This paper proposed a new explicit nonlinear dimensionality reduction using neural networks for image retrieval tasks. We first proposed a Quasi-curvature Locally Linear Embedding (QLLE) for training set. QLLE guarantees the linear…
When designing multispectral imaging systems for classifying different spectra it is necessary to choose a small number of filters from a set with several hundred different ones. Tackling this problem by full search leads to a tremendous…
In real world applications, uncertain parameters are the rule rather than the exception. We present a reachability algorithm for linear systems with uncertain parameters and inputs using set propagation of polynomial zonotopes. In contrast…
The paper develops the method for construction of families of particular solutions to some classes of nonlinear Partial Differential Equations (PDE). Method is based on the specific link between algebraic matrix equations and PDE.…
This paper is concerned with the low-rank approximation for large-scale nonsymmetric matrices. Inspired by the classical Nystrom method, which is a popular method to find the low-rank approximation for symmetric positive semidefinite…
Efficiently solving nonlinear equations underpins numerous scientific and engineering disciplines, yet scaling these solutions for challenging system models remains a challenge. This paper presents NonlinearSolve.jl -- a suite of…
We develop a novel, fundamental and surprisingly simple randomized iterative method for solving consistent linear systems. Our method has six different but equivalent interpretations: sketch-and-project, constrain-and-approximate, random…
Range aggregate queries find frequent application in data analytics. In some use cases, approximate results are preferred over accurate results if they can be computed rapidly and satisfy approximation guarantees. Inspired by a recent…
We present a new method for solving parametrized linear systems. Under certain assumptions on the parametrization, solutions to the linear systems for all parameters can be accurately approximated by linear combinations of solutions to…
We propose a new randomized method for solving systems of nonlinear equations, which can find sparse solutions or solutions under certain simple constraints. The scheme only takes gradients of component functions and uses Bregman…
A novel method, connecting the space of solutions of a linear differential equation, of arbitrary order, to the space of monomials, is used for exploring the algebraic structure of the solution space. Apart from yielding new expressions for…