Related papers: A note about high-order semi-implicit differentiat…
In this master's thesis, we introduce expansion systems as a general framework to describe a large variety of approximation algorithms, such as Taylor approximation, decimal expansion and continued fraction. We consider some basic…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
In this paper a novel hybrid approach for compensating the distortion of any interpolation has been proposed. In this hybrid method, a modular approach was incorporated in an iterative fashion. By using this approach we can get drastic…
We derive in this note a high-order corrector estimate for the homogenization of a microscopic semi-linear elliptic system posed in perforated domains. The major challenges are the presence of nonlinear volume and surface reaction rates.…
Quantization techniques have been applied in many challenging finance applications, including pricing claims with path dependence and early exercise features, stochastic optimal control, filtering problems and efficient calibration of large…
Stiff systems of ordinary differential equations (ODEs) arise in a wide range of scientific and engineering disciplines and are traditionally solved using implicit integration methods due to their stability and efficiency. However, these…
We present a novel parallel implementation for large-scale three-dimensional electromagnetic inversion based on a Gauss-Newton framework combined with a rational near-best approximation of the matrix exponential for transient simulations.…
Through introducing a new iterative formula for divided differnce using Neville's and Aitken's algorithms,we study new iterative methods for interpolation,numerical differentiation and numerical integration formulas with arbitrary order of…
In this paper we introduce an algebraic recursive multilevel incomplete factorization preconditioner, based on a distributed Schur complement formulation, for solving general linear systems. The novelty of the proposed method is to combine…
The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…
Splitting methods for the numerical integration of differential equations of order greater than two involve necessarily negative coefficients. This order barrier can be overcome by considering complex coefficients with positive real part.…
To solve the Cahn-Hilliard equation numerically, a new time integration algorithm is proposed, which is based on a combination of the Eyre splitting and the local iteration modified (LIM) scheme. The latter is employed to tackle the…
This work proposes a methodology to develop new numerical integration algorithms for ordinary differential equations based on state quantization, generalizing the notions of Linearly Implicit Quantized State Systems (LIQSS) methods. Using…
This article introduces an iterative method for solving nonsingular non-Hermitian positive semidefinite systems of linear equations. To construct the iteration process, the coefficient matrix is split into two non-Hermitian positive…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…
We extend the nonlocal operator method to higher order scheme by using a higher order Taylor series expansion of the unknown field. Such a higher order scheme improves the original nonlocal operator method proposed by the authors in [A…
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly discuss the target problem class, and introduce several…
Empirical risk minimization stands behind most optimization in supervised machine learning. Under this scheme, labeled data is used to approximate an expected cost (risk), and a learning algorithm updates model-defining parameters in search…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
This paper is part of a series of papers in which the asymptotic theory and appropriate symbolic computer code are developed to compute the asymptotic expansion of the solution of an n-th order ordinary differential equation. The paper…