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

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.

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Krylov subspace accelerated inexact Newton method for linear and nonlinear equations

Journal of Computational Chemistry ◽

10.1002/jcc.10108 ◽

2003 ◽

Vol 25 (3) ◽

pp. 328-334 ◽

Cited By ~ 25

Author(s):

Robert J. Harrison

Keyword(s):

Nonlinear Equations ◽

Newton Method ◽

Krylov Subspace ◽

Inexact Newton Method ◽

Linear And Nonlinear

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PARALLEL INCOMPLETE LU FACTORIZATION AS A PRECONDITIONER FOR KRYLOV SUBSPACE METHODS

Parallel Processing Letters ◽

10.1142/s0129626499000438 ◽

1999 ◽

Vol 09 (04) ◽

pp. 467-474 ◽

Cited By ~ 5

Author(s):

PATRICIA GONZALEZ ◽

JOSE C. CABALEIRO ◽

TOMAS F. PENA

Keyword(s):

Distributed Memory ◽

Krylov Subspace ◽

Krylov Subspace Methods ◽

New Method ◽

Lu Factorization ◽

Subspace Methods ◽

Multiprocessor Architectures ◽

Sparse Systems ◽

Incomplete Lu Factorization ◽

Final System

In this paper we describe a new method for the ILU(0) factorization of sparse systems in distributed memory multiprocessor architectures. This method uses a symbolic reordering technique, so the final system can be grouped in blocks where the rows are independent and the factorization of these entries can be carried out in parallel. The parallel ILU(0) factorization has been tested on the Cray T3E multicomputer using the MPI communication library. The performance was analysed using matrices from the Harwell–Boeing collection.

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Electromagnetic subsurface prospecting by a fully nonlinear multifocusing inexact Newton method

Journal of the Optical Society of America A ◽

10.1364/josaa.31.002618 ◽

2014 ◽

Vol 31 (12) ◽

pp. 2618 ◽

Cited By ~ 14

Author(s):

Marco Salucci ◽

Giacomo Oliveri ◽

Andrea Randazzo ◽

Matteo Pastorino ◽

Andrea Massa

Keyword(s):

Newton Method ◽

Inexact Newton Method ◽

Fully Nonlinear

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A Generalized Inexact Newton Method for Inverse Eigenvalue Problems

Abstract and Applied Analysis ◽

10.1155/2014/721346 ◽

2014 ◽

Vol 2014 ◽

pp. 1-6 ◽

Cited By ~ 1

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.

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