Related papers: Generalized Chebyshev acceleration on the unit dis…
Explicit time integration for immersed finite element discretizations severely suffers from the influence of poorly cut elements. In this contribution, we propose a generalized eigenvalue stabilization (GEVS) strategy for the element mass…
The theory of Chebyshev (uniform) approximation for univariate polynomial and piecewise polynomial functions has been studied for decades. The optimality conditions are based on the notion of alternating sequence. However, the extension the…
In this work, we propose a generalized alternating Anderson acceleration method, a periodic scheme composed of $t$ fixed-point iteration steps, interleaved with $s$ steps of Anderson acceleration with window size $m$, to solve linear and…
We present a class of algorithms based on rational Krylov methods to compute the action of a generalized matrix function on a vector. These algorithms incorporate existing methods based on the Golub-Kahan bidiagonalization as a special…
Deep unfolding is a promising deep-learning technique, whose network architecture is based on expanding the recursive structure of existing iterative algorithms. Although convergence acceleration is a remarkable advantage of deep unfolding,…
Generalized Chebyshev iteration (GCI) applied for solving linear equations with nonselfadjoint operators is considered. Sufficient conditions providing the convergence of iterations imposed on the domain of localization of the spectrum on…
The generalized perturbative approach is an all purpose variant of Stein's method used to obtain rates of normal approximation. Originally developed for functions of independent random variables this method is here extended to functions of…
Recent research has indicated a substantial rise in interest in understanding Nesterov's accelerated gradient methods via their continuous-time models. However, most existing studies focus on specific classes of Nesterov's methods, which…
This monograph covers some recent advances in a range of acceleration techniques frequently used in convex optimization. We first use quadratic optimization problems to introduce two key families of methods, namely momentum and nested…
Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…
In this paper we develop an optimisation based approach to multivariate Chebyshev approximation on a finite grid. We consider two models: multivariate polynomial approximation and multivariate generalised rational approximation. In the…
Some new rigorous perturbation bounds for the generalized Cholesky factorization with normwise or componentwise perturbations in the given matrix are obtained, where the componentwise perturbation has the form of backward rounding error for…
A generalization of the Newton-based matrix splitting iteration method (GNMS) for solving the generalized absolute value equations (GAVEs) is proposed. Under mild conditions, the GNMS method converges to the unique solution of the GAVEs.…
Chebyshev interpolation is a highly effective, intensively studied method and enjoys excellent numerical properties. The interpolation nodes are known beforehand, implementation is straightforward and the method is numerically stable. For…
In this paper, we apply acceleration to the inverse-free preconditioned Krylov subspace method introduced by Golub and Ye, which solves the symmetric generalized eigenvalue problem for the algebraically smallest eigenvalue. As the method is…
The Kaczmarz method is an iterative numerical method for solving large and sparse rectangular systems of linear equations. Gearhart, Koshy and Tam have developed an acceleration technique for the Kaczmarz method that minimizes the distance…
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…
The incremental aggregated gradient algorithm is popular in network optimization and machine learning research. However, the current convergence results require the objective function to be strongly convex. And the existing convergence…
This paper presents an algorithm to simulate Gaussian random vectors whose precision matrix can be expressed as a polynomial of a sparse matrix. This situation arises in particular when simulating Gaussian Markov random fields obtained by…
By incorporating a new matrix splitting and the momentum acceleration into the relaxed-based matrix splitting (RMS) method \cite{soso2023}, a generalization of the RMS (GRMS) iterative method for solving the generalized absolute value…