NEP-PACK

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

M(λ)v=0

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> ]
(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)
• 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