Related papers: A Matrix Decomposition Method for Odd-Type Gaussia…
In this article we present an algorithm to efficiently evaluate the exchange matrix in periodic systems when Gaussian basis set with pseudopotentials are used. The usual algorithm for evaluating exchange matrix scales cubically with the…
Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…
Gabidulin codes, originally defined over finite fields, are an important class of rank metric codes with various applications. Recently, their definition was generalized to certain fields of characteristic zero and a Welch--Berlekamp like…
A representation of finite fields that has proved useful when implementing finite field arithmetic in hardware is based on an isomorphism between subrings and fields. In this paper, we present an unified formulation for multiplication in…
Decomposing an algebraic variety into irreducible or equidimensional components is a fundamental task in classical algebraic geometry and has various applications in modern geometry engineering. Several researchers studied the problem and…
We explore new approaches for finding matrix multiplication algorithms in the commutative setting by adapting the flip graph technique: a method previously shown to be effective for discovering fast algorithms in the non-commutative case.…
We present an algorithm for the integrand-level reduction of multi-loop amplitudes of renormalizable field theories, based on computational algebraic geometry. This algorithm uses (1) the Gr\"obner basis method to determine the basis for…
Composite function minimization captures a wide spectrum of applications in both computer vision and machine learning. It includes bound constrained optimization and cardinality regularized optimization as special cases. This paper proposes…
We exploit the truncated singular value decomposition and the recently proposed circulant decomposition for an efficient first-order approximation of the multiplication of large dense matrices. A decomposition of each matrix into a sum of a…
The Gaussian beam superposition method is an asymptotic method for computing high frequency wave fields in smoothly varying inhomogeneous media. In this paper we study the accuracy of the Gaussian beam superposition method and derive error…
In geostatistics, traditional spatial models often rely on the Gaussian Process (GP) to fit stationary covariances to data. It is well known that this approach becomes computationally infeasible when dealing with large data volumes,…
The rigorous solution to the grating diffraction problem is a cornerstone step in many scientific fields and industrial applications ranging from the study of the fundamental properties of metasurfaces to the simulation of photolithography…
This paper addresses the gradient coding and coded matrix multiplication problems in distributed optimization and coded computing. We present a numerically stable binary coding method which overcomes the drawbacks of the \textit{Fractional…
We present a novel approach for model reduction of nonlinear dynamical systems based on proper orthogonal decomposition (POD). Our method, derived from Density Matrix Renormalization Group (DMRG), provides a significant reduction in…
We study the computational complexity of a very basic problem, namely that of finding solutions to a very large set of random linear equations in a finite Galois Field modulo q. Using tools from statistical mechanics we are able to identify…
We give explicit low-rank bilinear non-commutative schemes for multiplying structured $n \times n$ matrices with $2 \leq n \leq 5$, which serve as building blocks for recursive algorithms with improved multiplicative factors in asymptotic…
Mutually unbiased bases are an important tool in many applications of quantum information theory. We present a new algorithm for finding the mutually unbiased bases for two-qubit systems. We derive a system of four equations in the Galois…
The Galerkin difference (GD) basis is a set of continuous, piecewise polynomials defined using a finite difference like grid of degrees of freedom. The one dimensional GD basis functions are naturally extended to multiple dimensions using…
In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can…
Gaussian Markov random fields (GMRFs) are useful in a broad range of applications. In this paper we tackle the problem of learning a sparse GMRF in a high-dimensional space. Our approach uses the l1-norm as a regularization on the inverse…