Related papers: A survey of scalar and vector extrapolation
This paper introduces a new mathematical framework for analysis and optimization of tensor expressions within an enclosing loop. Tensors are multi-dimensional arrays of values. They are common in high performance computing (HPC) and machine…
Motivated by machine learning problems over large data sets and distributed optimization over networks, we develop and analyze a new method called incremental Newton method for minimizing the sum of a large number of strongly convex…
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families of stable finite element pairs and on the availability of…
Abstraction, counterexample-guided refinement, and interpolation are techniques that are essential to the success of predicate-based program analysis. These techniques have not yet been applied together to explicit-value program analysis.…
We investigate an interpolation/extrapolation method that, given scattered observations of the Fourier transform, approximates its inverse. The interpolation algorithm takes advantage of modelling the available data via a shape-driven…
We propose a simple technique that, if combined with algorithms for computing functions of triangular matrices, can make them more efficient. Basically, such a technique consists in a specific scaling similarity transformation that reduces…
Nonlinear acceleration algorithms improve the performance of iterative methods, such as gradient descent, using the information contained in past iterates. However, their efficiency is still not entirely understood even in the quadratic…
We investigate possibilities to speed up iterative algorithms for non-blind image deconvolution. We focus on algorithms in which convolution with the point-spread function to be deconvolved is used in each iteration, and aim at accelerating…
We introduce novel convergence results for asynchronous iterations that appear in the analysis of parallel and distributed optimization algorithms. The results are simple to apply and give explicit estimates for how the degree of asynchrony…
The matrix exponential is a fundamental operator in scientific computing and system simulation, with applications ranging from control theory and quantum mechanics to modern generative machine learning. While Pad\'e approximants combined…
Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…
With origins in game theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more.…
Approximate solutions of Urysohn integral equations using projection methods involve integrals which need to be evaluated using a numerical quadrature formula. It gives rise to the discrete versions of the projection methods. For $r \geq…
The quest for an algorithm that solves an $n\times n$ linear system in $O(n^2)$ time complexity, or $O(n^2 \text{poly}(1/\epsilon))$ when solving up to $\epsilon$ relative error, is a long-standing open problem in numerical linear algebra…
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…
This paper introduces a sparse matrix discrete interpolation method to effectively compute matrix approximations in the reduced order modeling framework. The sparse algorithm developed herein relies on the discrete empirical interpolation…
We provide a primer to numerical methods based on Taylor series expansions such as generalized finite difference methods and collocation methods. We provide a detailed benchmarking strategy for these methods as well as all data files…
The problem of parameter estimation from a standard vector linear regression equation in the absence of sufficient excitation in the regressor is addressed. The first step to solve the problem consists in transforming this equation into a…
We consider a Urysohn integral operator $\mathcal{K}$ with kernel of the type of Green's function. For $r \geq 1$, a space of piecewise polynomials of degree $\leq r-1 $ with respect to a uniform partition is chosen to be the approximating…
The error exponent in lossy source coding characterizes the asymptotic decay rate of error probability with respect to blocklength. The Marton's error exponent provides the theoretically optimal bound on this rate. However, computation…