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# NEP-PACK

A nonlinear eigenvalue problem is the problem to determine a scalar λ and a vector v such that

M(λ)v=0

where M is an nxn-matrix depending on a parameter. This package aims to provide state-of-the-art algorithms to solve this problem, as well as a framework to formulate applications and easy access to benchmark problems. This currently includes (but is not restricted to) Newton-type methods, Subspace methods, Krylov methods, contour integral methods, block methods, companion matrix approaches. Problem transformation techniques such as scaling, shifting, deflating are also natively supported by the package.

# How to use it?

On Julia 1.X and Julia 0.7, install it as a registered package by typing `] add ...` at the REPL-prompt:

``````julia> ]
``````

After that, check out "Getting started" in

NEP-PACK online user's guide

## GIT Version

If you want the cutting edge development version and not the latest release, install it with the URL:

``````julia> ]
``````

## NEP solvers

Features and solvers (see documentation https://nep-pack.github.io/NonlinearEigenproblems.jl/methods/ for further information and references):

• Arnoldi/Krylov type
• NLEIGS
• Infinite Arnoldi method: (iar)
• Tensor infinite Arnoldi method (tiar)
• Infinite bi-Lanczos (infbilanczos)
• Infinite Lanczos (ilan)
• Projection methods
• Jacobi-Davidson (jd_effenberger)
• Jacobi-Davidson (jd_betcke)
• Nonlinear Arnoldi method (nlar)
• Common Rayleigh-Ritz projection interface
• Contour integral methods
• Beyn's contour integral method
• Block SS (Higher moments) contour integral method of Asakura & Sakurai
• Common quadrature interface for parallelization
• Newton & Rayleigh type:
• Classical Newton-Raphson
• Augmented Newton
• Residual inverse iteration
• Quasi-Newton
• Block Newton
• Rayleigh functional iteration (RFI a, b)
• Newton-QR
• Implicit determinant method
• Broyden's method
• Companion matrices
• First companion form
• Companion form for Chebyshev polynomials
• Other
• Chebyshev interpolation
• Transformations
• Rayleigh-Ritz (`ProjNEP` and `inner_solve`)
• Deflation (Effenberger style)

# Development

Core developers (alphabetical): Max Bennedich, Elias Jarlebring (www.math.kth.se/~eliasj), Giampaolo Mele (www.math.kth.se/~gmele), Emil Ringh (www.math.kth.se/~eringh), Parikshit Upadhyaya (https://www.kth.se/profile/pup/). Thanks to A Koskela for involvement in initial version of the software.

# How to cite

If you find this software useful please cite

``````@Misc{,
author =   {E. Jarlebring and M. Bennedich and G. Mele and E. Ringh and P. Upadhyaya},
title =    {{NEP-PACK}: A {Julia} package for nonlinear eigenproblems},
year =     {2018},
note =     {https://github.com/nep-pack},
eprint = {arXiv:1811.09592},
}
``````

If you use a specific method, please also give credit to the algorithm researcher. Reference to a corresponding algorithm paper can be found by in, e.g., by writing `?resinv`.

Some links below are developer info on KTH. We will migrate them soon:

05/25/2018

10 days ago

2965 commits