Preconditioned steepest descent-like methods for symmetric indefinite systems
نویسندگان
چکیده
منابع مشابه
A Geometric Convergence Theory for the Preconditioned Steepest Descent Iteration
Preconditioned gradient iterations for very large eigenvalue problems are efficient solvers with growing popularity. However, only for the simplest preconditioned eigensolver, namely the preconditioned gradient iteration (or preconditioned inverse iteration) with fixed step size, sharp non-asymptotic convergence estimates are known. These estimates require a properly scaled preconditioner. In t...
متن کاملSymmetric indefinite systems for interior point methods
We present a unified framework for solving linear and convex quadratic programs via interior point methods. At each iteration, this method solves an indefinite system whose matrix is [_~-2 A v] instead of reducing to obtain the usual AD2A v system. This methodology affords two advantages: (1) it avoids the fill created by explicitly forming the product AD2A v when A has dense columns; and (2) i...
متن کاملPreconditioned steepest descent methods for some nonlinear elliptic equations involving p-Laplacian terms
Article history: Received 6 July 2016 Received in revised form 2 December 2016 Accepted 23 December 2016 Available online 28 December 2016
متن کاملMann-type Steepest-descent and Modified Hybrid Steepest-descent Methods for Variational Inequalities in Banach Spaces
1Department of Mathematics, Shanghai Normal University, Shanghai; and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai, China 2Department of Mathematics & Statistics, College of Science, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia; and Department of Mathematics, Aligarh Muslim University, Aligarh, India 3Department of Applied Mathematics, National S...
متن کاملOn Spectral Properties of Steepest Descent Methods
In recent years it has been made more and more clear that the critical issue in gradient methods is the choice of the step length, whereas using the gradient as search direction may lead to very effective algorithms, whose surprising behaviour has been only partially explained, mostly in terms of the spectrum of the Hessian matrix. On the other hand, the convergence of the classical Cauchy stee...
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: Linear Algebra and its Applications
سال: 2016
ISSN: 0024-3795
DOI: 10.1016/j.laa.2016.09.011