Related papers: Faster Sparse Multivariate Polynomial Interpolatio…
Convolutional sparse representations are a form of sparse representation with a dictionary that has a structure that is equivalent to convolution with a set of linear filters. While effective algorithms have recently been developed for the…
We consider the disjoint bilinear programming problem in which one of the disjoint subsets has the structure of an acute-angled polytope. An optimality criterion for such a problem is formulated and proved, and based on this, a polynomial…
We present new, practical algorithms for the hypersurface implicitization problem: namely, given a parametric description (in terms of polynomials or rational functions) of the hypersurface, find its implicit equation. Two of them are for…
The Kaczmarz algorithm is a popular solver for overdetermined linear systems due to its simplicity and speed. In this paper, we propose a modification that speeds up the convergence of the randomized Kaczmarz algorithm for systems of linear…
We settle the computational complexity of fundamental questions related to multicriteria integer linear programs, when the dimensions of the strategy space and of the outcome space are considered fixed constants. In particular we construct:…
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem…
Sparse approximations using highly over-complete dictionaries is a state-of-the-art tool for many imaging applications including denoising, super-resolution, compressive sensing, light-field analysis, and object recognition. Unfortunately,…
Polynomial multiplication is known to have quasi-linear complexity in both the dense and the sparse cases. Yet no truly linear algorithm has been given in any case for the problem, and it is not clear whether it is even possible. This…
Linear optimization problems are investigated whose parameters are uncertain. We apply coherent distortion risk measures to capture the possible violation of a restriction. Each risk constraint induces an uncertainty set of coefficients,…
We develop a local polynomial spline interpolation scheme for arbitrary spline order on bounded intervals. Our method's local formulation, effective boundary considerations and optimal interpolation error rate make it particularly useful…
We present a new formula for divided difference and few new schemes of divided difference tables in this paper. Through this, we derive new interpolation, numerical differentiation and numerical integration formulas with arbitrary order of…
Variable selection is a procedure to attain the truly important predictors from inputs. Complex nonlinear dependencies and strong coupling pose great challenges for variable selection in high-dimensional data. In addition, real-world…
We conducted an extensive computational experiment, lasting multiple CPU-years, to optimally select parameters for two important classes of algorithms for finding sparse solutions of underdetermined systems of linear equations. We make the…
We introduce a new technique for solving uni-parametric versions of linear programs, convex quadratic programs, and linear complementarity problems in which a single parameter is permitted to be present in any of the input data. We…
This paper presents fast first-order methods for solving linear programs (LPs) approximately. We adapt online linear programming algorithms to offline LPs and obtain algorithms that avoid any matrix multiplication. We also introduce a…
Based on tensor neural network, we propose an interpolation method for high dimensional non-tensor-product-type functions. This interpolation scheme is designed by using the tensor neural network based machine learning method. This means…
Integer Linear Programming with $n$ binary variables and $m$ many $0/1$-constraints can be solved in time $2^{\tilde O(m^2)} \text{poly}(n)$ and it is open whether the dependence on $m$ is optimal. Several seemingly unrelated problems,…
Algebraic characterization of logic programs has received increasing attention in recent years. Researchers attempt to exploit connections between linear algebraic computation and symbolic computation in order to perform logical inference…
Finding the sparse representation of a signal in an overcomplete dictionary has attracted a lot of attention over the past years. This paper studies ProSparse, a new polynomial complexity algorithm that solves the sparse representation…
Image interpolation is a special case of image super-resolution, where the low-resolution image is directly down-sampled from its high-resolution counterpart without blurring and noise. Therefore, assumptions adopted in super-resolution…