A Convergence Analysis of the Peaceman--Rachford Scheme for Semilinear Evolution Equations
نویسندگان
چکیده
منابع مشابه
A Convergence Analysis of the Peaceman-Rachford Scheme for Semilinear Evolution Equations
The Peaceman–Rachford scheme is a commonly used splitting method for discretizing semilinear evolution equations, where the vector fields are given by the sum of one linear and one nonlinear dissipative operator. Typical examples of such equations are reaction-diffusion systems and the damped wave equation. In this paper we conduct a convergence analysis for the Peaceman– Rachford scheme in the...
متن کاملConvergence analysis of the Peaceman-Rachford splitting method for nonsmooth convex optimization
In this paper, we focus on the convergence analysis for the application of the PeacemanRachford splitting method to a convex minimization model whose objective function is the sum of a smooth and nonsmooth convex functions. The sublinear convergence rate in term of the worst-case O(1/t) iteration complexity is established if the gradient of the smooth objective function is assumed to be Lipschi...
متن کاملConvergence Rate Analysis of the Forward-Douglas-Rachford Splitting Scheme
Operator splitting schemes are a class of powerful algorithms that solve complicated monotone inclusion and convex optimization problems that are built from many simpler pieces. They give rise to algorithms in which all simple pieces of the decomposition are processed individually. This leads to easily implementable and highly parallelizable or distributed algorithms, which often obtain nearly ...
متن کاملStochastic Strictly Contractive Peaceman-Rachford Splitting Method
In this paper, we propose a couple of new Stochastic Strictly Contractive PeacemanRachford Splitting Method (SCPRSM), called Stochastic SCPRSM (SS-PRSM) and Stochastic Conjugate Gradient SCPRSM (SCG-PRSM) for large-scale optimization problems. The two types of Stochastic PRSM algorithms respectively incorporate stochastic variance reduced gradient (SVRG) and conjugate gradient method. Stochasti...
متن کاملStability and Convergence of the Peaceman-Rachford ADI Method for Initial-Boundary Value Problems
In this paper an analysis will be presented for the ADI (alternating direction implicit) method of Peaceman and Rachford applied to initial-boundary value problems for partial differential equations in two space dimensions. We shall use the method of lines approach. Motivated by developments in the field of stiff nonlinear ordinary differential equations, our analysis will focus on problems whe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2013
ISSN: 0036-1429,1095-7170
DOI: 10.1137/120890570