Related papers: Two-step General Linear Methods for Retarded Funct…
Recently, there has been growing interest in developing optimization methods for solving large-scale machine learning problems. Most of these problems boil down to the problem of minimizing an average of a finite set of smooth and strongly…
In this work, we further investigate the application of the well-known Richardson extrapolation (RE) technique to accelerate the convergence of sequences resulting from linear multistep methods (LMMs) for numerically solving initial-value…
New problem is considered that is to find nonlinear differential equations with special solutions. Method is presented to construct nonlinear ordinary differential equations with exact solution. Crucial step to the method is the assumption…
Some fractional Newton methods have been proposed in order to find roots of nonlinear equations using fractional derivatives. In this paper we introduce a fractional Newton method with order $\alpha+1$ and compare with another fractional…
General solutions of nonlinear ordinary differential equations (ODEs) are in general difficult to find although powerful integrability techniques exist in the literature for this purpose. It has been shown that in some scalar cases…
In this paper, we propose an acceleration framework for a class of iterative methods using the Reduced Order Method (ROM). Assuming that the underlying iterative scheme generates a rich basis for the solution space, we construct the next…
In this study, we introduce a refined method for ascertaining error estimations in numerical simulations of dynamical systems via an innovative application of composition techniques. Our approach involves a dual application of a basic…
We present a numerical method for the approximation of solutions for the class of stochastic differential equations driven by Brownian motions which induce stochastic variation in fixed directions. This class of equations arises naturally…
In this manuscript we propose and analyze an implicit two-point type method (or inertial method) for obtaining stable approximate solutions to linear ill-posed operator equations. The method is based on the iterated Tikhonov (iT) scheme. We…
We propose a new family of multilevel methods for unconstrained minimization. The resulting strategies are multilevel extensions of high-order optimization methods based on q-order Taylor models (with q >= 1) that have been recently…
A solution of two-stage stochastic generalized equations is a pair: a first stage solution which is independent of realization of the random data and a second stage solution which is a function of random variables.This paper studies…
We provide a mathematical framework for studying different versions of discontinuous Galerkin (DG) approaches for solving 2D Riemann-Liouville fractional elliptic problems on a finite domain. The boundedness and stability analysis of the…
This article develops an approximate proximal approach for the generalized method of lines. The present results are extensions and applications of previous ones which have been published since 2011, in books and articles such as [3,4,5,6].…
To broaden the range of applicability of variable-order fractional differential models, reliable numerical approaches are needed to solve the model equation. In this paper, we develop Laguerre spectral collocation methods for solving…
This paper presents a general framework of high-order finite difference (HFD) schemes for the tempered fractional Laplacian (TFL) based on new generating functions obtained from the discrete symbols. Specifically, for sufficiently smooth…
Classification on long-tailed distributed data is a challenging problem, which suffers from serious class-imbalance and hence poor performance on tail classes with only a few samples. Owing to this paucity of samples, learning on the tail…
We present a successive constraint approach that makes it possible to cheaply solve large-scale linear matrix inequalities for a large number of parameter values. The efficiency of our method is made possible by an offline/online…
The asymptotic iteration method (AIM) is an iterative technique used to find exact and approximate solutions to second-order linear differential equations. In this work, we employed AIM to solve systems of two first-order linear…
In this paper, we propose new linearly convergent second-order methods for minimizing convex quartic polynomials. This framework is applied for designing optimization schemes, which can solve general convex problems satisfying a new…
We generalize the theory of underlying one-step methods to strictly stable general linear methods (GLMs) solving nonautonomous ordinary differential equations (ODEs) that satisfy a global Lipschitz condition. We combine this theory with the…