Krylov subspace accelerated inexact Newton method for linear and nonlinear equations

2003 ◽  
Vol 25 (3) ◽  
pp. 328-334 ◽  
Author(s):  
Robert J. Harrison
Keyword(s):  
Nonlinear Equations ◽  
Newton Method ◽  
Krylov Subspace ◽  
Inexact Newton Method ◽  
Linear And Nonlinear

Inexact Newton method for the solution of eigenproblems arising in hydrodynamic temporal stability analysis

2020 ◽  
Vol 28 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Kirill V. Demyanko ◽  
Igor E. Kaporin ◽  
Yuri M. Nechepurenko
Keyword(s):  
Stability Analysis ◽  
Newton Method ◽  
Krylov Subspace ◽  
Hermitian Matrix ◽  
Temporal Stability ◽  
Inexact Newton Method ◽  
Lu Factorization ◽  
Matrix Pencils ◽  
Deflating Subspaces ◽  
Incomplete Lu Factorization

AbstractThe inexact Newton method developed earlier for computing deflating subspaces associated with separated groups of finite eigenvalues of regular linear large sparse non-Hermitian matrix pencils is specialized to solve eigenproblems arising in the hydrodynamic temporal stability analysis. To this end, for linear systems to be solved at each step of the Newton method, a new efficient MLILU2 preconditioner based on the multilevel 2nd order incomplete LU-factorization is proposed. A special variant of Krylov subspace method IDR2 with right preconditioning is developed. In comparison with GMRES it requires much smaller workspace while may converge considerably faster than BiCGStab. The effectiveness of the proposed methods is illustrated with matrix pencils of order up to 3.1 ⋅ 106 arising in the temporal linear stability analysis of a typical hydrodinamic flow.

Electromagnetic subsurface prospecting by a fully nonlinear multifocusing inexact Newton method

2014 ◽  
Vol 31 (12) ◽  
pp. 2618 ◽  
Author(s):  
Marco Salucci ◽  
Giacomo Oliveri ◽  
Andrea Randazzo ◽  
Matteo Pastorino ◽  
Andrea Massa
Keyword(s):  
Newton Method ◽  
Inexact Newton Method ◽  
Fully Nonlinear

Some variational principles associated with ODEs of maximal symmetry. Part 2: The general case

2018 ◽  
Vol 24 (2) ◽  
pp. 175-183
Author(s):  
Jean-Claude Ndogmo
Keyword(s):  
Explicit Form ◽  
Nonlinear Equations ◽  
Variational Principles ◽  
Symmetry Algebra ◽  
First Integrals ◽  
Maximal Symmetry ◽  
General Order ◽  
Linear And Nonlinear ◽  
Variational Symmetries ◽  
Variational Symmetry

Abstract Variational and divergence symmetries are studied in this paper for the whole class of linear and nonlinear equations of maximal symmetry, and the associated first integrals are given in explicit form. All the main results obtained are formulated as theorems or conjectures for equations of a general order. A discussion of the existence of variational symmetries with respect to a different Lagrangian, which turns out to be the most common and most readily available one, is also carried out. This leads to significantly different results when compared with the former case of the transformed Lagrangian. The latter analysis also gives rise to more general results concerning the variational symmetry algebra of any linear or nonlinear equations.

scholarly journals A Generalized Inexact Newton Method for Inverse Eigenvalue Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weiping Shen
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Eigenvalue Problems ◽  
Generalized Newton Method ◽  
Inexact Newton Method ◽  
Numerical Tests ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue ◽  
Generalized Newton ◽  
Special Case

We propose a generalized inexact Newton method for solving the inverse eigenvalue problems, which includes the generalized Newton method as a special case. Under the nonsingularity assumption of the Jacobian matrices at the solutionc*, a convergence analysis covering both the distinct and multiple eigenvalue cases is provided and the quadratic convergence property is proved. Moreover, numerical tests are given in the last section and comparisons with the generalized Newton method are made.

scholarly journals GPU-Based Fast Decoupled Power Flow With Preconditioned Iterative Solver and Inexact Newton Method

2017 ◽  
Vol 32 (4) ◽  
pp. 2695-2703 ◽  
Author(s):  
Xue Li ◽  
Fangxing Li ◽  
Haoyu Yuan ◽  
Hantao Cui ◽  
Qinran Hu
Keyword(s):  
Newton Method ◽  
Power Flow ◽  
Inexact Newton Method ◽  
Iterative Solver ◽  
Preconditioned Iterative

scholarly journals The variational iteration method for solving n-th order fuzzy differential equations

Open Physics ◽  
2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Hossein Jafari ◽  
Mohammad Saeidy ◽  
Dumitru Baleanu
Keyword(s):  
Differential Equations ◽  
Nonlinear Equations ◽  
Analytical Method ◽  
Iteration Method ◽  
Initial Conditions ◽  
Variational Iteration Method ◽  
Linear Differential Equations ◽  
Variational Iteration ◽  
Linear And Nonlinear ◽  
Linear Differential

AbstractThe variational iteration method (VIM) proposed by Ji-Huan He is a new analytical method for solving linear and nonlinear equations. In this paper, the variational iteration method has been applied in solving nth-order fuzzy linear differential equations with fuzzy initial conditions. This method is illustrated by solving several examples.

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