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A method is proposed for solving equality constrained nonlinear optimization problems involving twice continuously differentiable functions. The method employs a trust funnel approach consisting of two phases: a first phase to locate an…
In this paper, we propose a new stochastic column-block gradient descent method for solving nonlinear systems of equations. It has a descent direction and holds an approximately optimal step size obtained through an optimization problem. We…
We aim at computing the derivative of the solution to a parametric optimization problem with respect to the involved parameters. For a class broader than that of strongly convex functions, this can be achieved by automatic differentiation…
In this paper we construct a third order method for solving additively split autonomous stiff systems of ordinary differential equations. The constructed additive method is L-stable with respect to the implicit part and allows to use an…
A version of the Dynamical Systems Gradient Method for solving ill-posed nonlinear monotone operator equations is studied in this paper. A discrepancy principle is proposed and justified. A numerical experiment was carried out with the new…
We introduce basic aspects of new operator method, which is very suitable for practical solving differential equations of various types. The main advantage of the method is revealed in opportunity to find compact exact operator solutions of…
In this work we introduce a new family of twelve-step linear multistep methods for the integration of the Schr\"odinger equation. The new methods are constructed by adopting a new methodology which improves the phase lag characteristics by…
We propose a new class of rigorous methods for derivative-free optimization with the aim of delivering efficient and robust numerical performance for functions of all types, from smooth to non-smooth, and under different noise regimes. To…
We present iterative solvers to approximate the solution of numerical schemes for stochastic Stefan problems. After briefly talking about the convergence results, we tackle the question of efficient strategies for solving the nonlinear…
This paper presents and investigates an inexact proximal gradient method for solving composite convex optimization problems characterized by an objective function composed of a sum of a full-domain differentiable convex function and a…
Recent advances (Sherman, 2017; Sidford and Tian, 2018; Cohen et al., 2021) have overcome the fundamental barrier of dimension dependence in the iteration complexity of solving $\ell_\infty$ regression with first-order methods. Yet it…
We prove convergence with optimal algebraic rates for an adaptive finite element method for nonlinear equations with strongly monotone operator. Unlike prior works, our analysis also includes the iterative and inexact solution of the…
This is the first in a series of papers which deal with the development of novel methods for solving a system of linear algebraic equations with a time complexity lower than existing algorithms. The NxN system of linear equations, Ax = b,…
We introduce generalised finite difference methods for solving fully nonlinear elliptic partial differential equations. Methods are based on piecewise Cartesian meshes augmented by additional points along the boundary. This allows for…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
The unsupervised task of aligning two or more distributions in a shared latent space has many applications including fair representations, batch effect mitigation, and unsupervised domain adaptation. Existing flow-based approaches estimate…
A new one-parameter family of iterative method for solving nonlinear equations is constructed and studied. Two variants, both with cubic convergence, are developed, one for finding simple zeros and other for multiple zeros of known…
We present a simple yet powerful technique for forming iterative methods of various convergence orders. Methods of various convergence orders (four, six, eight and ten) are formed through a modest modification of the classical Newton…
The three-step alternating iteration scheme for finding an iterative solution of a singular (non-singular) linear systems in a faster way was introduced by Nandi {\it et al.} [Numer. Algorithms; 84 (2) (2020) 457-483], recently. The authors…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…