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, install it as a registered package by typing ] add ... at the REPL-prompt:

julia> ]
(v1.0) pkg> add NonlinearEigenproblems

After that, check out "Getting started" in

NEP-PACK online user's guide

or read the preprint: https://arxiv.org/abs/1811.09592

GIT Version

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

julia> ]
(v1.0) pkg> add git://github.com/nep-pack/NonlinearEigenproblems.jl.git

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)
  • AAA CORK (AAAeigs)
• 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)
  • Problem gallery (including access to the NLEVP-gallery)
  • 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:

• NEP-page style "guide": https://github.com/nep-pack/NonlinearEigenproblems.jl/wiki/Style-guidelines-and-notes

• GIT-workflow: https://github.com/nep-pack/NonlinearEigenproblems.jl/wiki/Git-workflow

• GIT-usage @ KTH: https://gitr.sys.kth.se/nep-pack/nep-pack-alpha/wiki

• NEP-methods @ KTH: https://gitr.sys.kth.se/nep-pack/nep-pack-alpha/wiki/NEP-methods

• NEP-applications @ KTH: https://gitr.sys.kth.se/nep-pack/nep-pack-alpha/wiki/Applications