Related papers: A simple way to speedup Gauss Elimination

Gaussian Splatting (GS) has emerged as a dominating technique for image rendering and has quickly been adapted for the X-ray Computed Tomography (CT) reconstruction task. However, despite being on par or better than many of its…

Urban and Bierman introduced a calculus of proof terms for the sequent calculus LK with a strongly normalizing reduction relation. We extend this calculus to simply-typed higher-order logic with inferences for induction and equality, albeit…

This paper presents a theorem which solves the problem of reduction of the determinant order by means of a transformation of it, into other determinant whose each element are a determinant of second order. This implies that, if the process…

Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…

Stochastic composition optimization draws much attention recently and has been successful in many emerging applications of machine learning, statistical analysis, and reinforcement learning. In this paper, we focus on the composition…

Variable Elimination is a fundamental algorithm for probabilistic inference over Bayesian networks. In this paper, we propose a novel materialization method for Variable Elimination, which can lead to significant efficiency gains when…

Gaussian boson sampling is a promising model for demonstrating quantum computational supremacy, which eases the experimental challenge of the standard boson-sampling proposal. Here by analyzing the computational costs of classical…

It is commonly believed that decoherence is the main obstacle to quantum information processing. In contrast to this, we show how decoherence in the form of dissipation can improve the performance of certain quantum gates. As an example we…

In this paper, we obtain various series and asymptotic expansions involving the modified Bessel function of the second kind for the normal inverse Gaussian cumulative distribution function. The new expansions accelerate computations,…

We provide a rather general and very simple to compute lower bound for the asymptotic convergence factor of compact subsets of the set of complex numbers with connected complement and finitely many connected components .

Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here,…

We provide a numerical scheme to approximate as closely as desired the Gaussian or exponential measure $\mu(\om)$ of (not necessarily compact) basic semi-algebraic sets$\om\subset\R^n$. We obtain two monotone (non increasing and non…

We consider the uniform asymptotic expansion for the Gauss hypergeometric function \[{}_2F_1(a+\epsilon\lambda,b;c+\lambda;x),\qquad 0<x<1\] as $\lambda\to+\infty$ in the neigbourhood of $\epsilon x=1$ when the parameter $\epsilon>1$ and…

We study accelerated optimization methods in the Gaussian phase retrieval problem. In this setting, we prove that gradient methods with Polyak or Nesterov momentum have similar implicit regularization to gradient descent. This implicit…

In this paper we propose a new fast splitting algorithm to solve the Weighted Split Bregman minimization problem in the backward step of an accelerated Forward-Backward algorithm. Beside proving the convergence of the method, numerical…

In this paper, we propose an acceleration of the exact k-means++ algorithm using geometric information, specifically the Triangle Inequality and additional norm filters, along with a two-step sampling procedure. Our experiments demonstrate…

Extending Bayesian optimization to batch evaluation can enable the designer to make the most use of parallel computing technology. However, most of current batch approaches do not scale well with the batch size. That is, their performances…

A continuous analog of Gauss-Newton method for solving nonlinear ill-posed problems is proposed. Its converegence is proved. A numerical example is presented to demonstrate efficiency of the propsed method.

In recent times, the utilization of 3D models has gained traction, owing to the capacity for end-to-end training initially offered by Neural Radiance Fields and more recently by 3D Gaussian Splatting (3DGS) models. The latter holds a…

This paper deals with speeding up the convergence of a class of two-step iterative methods for solving linear systems of equations. To implement the acceleration technique, the residual norm associated with computed approximations for each…