About

This website hosts a collection of benchmark instances for the Eigenvector-dependent Nonlinear Eigenvalue Problems (NEPv).

NEPv have been intensively studied in the scientific literature. They arise in various applications and come in a variety of forms. The primary goal of NEPvLib is to provide researchers with easy access to those problems and serve the research community regarding testing and evaluating the analysis and computation of NEPv.

All the benchmark instances in NEPvLib are gathered from existing publications pertinent to NEPv research. NEPvLib is an actively growing collection of NEPv, and new problems will be added once available.

Format

All the NEPv generators are provided as MATLAB functions, with information on the underlying problems detailed in the header of each function file. Several solution algorithms are also available for particular NEPv.

Individual NEPv can be accessed through the list of Problem Sets below, where a description of the form of NEPv, with problem features and the application backgrounds, are provided.

Problem Sets

• Gross-Pitaevskii: 2D discrete Gross-Pitaevskii equations from Bose–Einstein condensation.

  • NEPv form: \(H(x) x = \lambda x\), \(x^Hx=1\).

  • Key features: Smallest eigenvalue \(\lambda\); Hermitian; Unitarily invariant.

  • Download: dgp2d.m

• Kohn-Sham: A discrete Kohn-Sham equation from electronic structure calculation.

  • NEPv form: \(H(X) X = X\Lambda\), \(X^TX=I_k\)

  • Key features: Block \(X\in\mathbb R^{n\times k}\); \(\Lambda\) contains \(k\) smallest eigenvalue; Symmetric; Unitarily invariant.

  • Download: dks.m

• Monotone NEPv: A collection of monotone NEPv.

  • NEPv form: \(H(x) x = \lambda x\), \(x^Hx=1\).

  • Key features: Largest eigenvalue \(\lambda\); Hermitian; Symmetric; Unitarily invariant; Multiple solution; SCF global convergence.

  • Download:

    • Numerical radius: numrd.m

    • Tensor rank-1 approximation: tensor.m; Data matrices fb20.mat, princeton.mat, reuters.mat.

    • Distance to singularity of dHDAE: dhdae.m

• Robust Rayleigh quotient: A collection of NEPv from robust quotient optimization.

  • NEPv form: \(G(x) x = \lambda H(x)x\), \(x^Tx=1\).

  • Key features: Smallest Positive eigenvalue \(\lambda\); Symmetric; Unitarily invariant; SCF quadratic convergence.

  • Download:

    • Robust Eigenvalue Classification: rgec.m; Data matrices pima.mat, rng.mat

    • Robust Fisher's LDA: rlda.m; Data matrices sonar.mat, inosphere.mat

    • Robust Spatial Pattern Analysis: rcsp.m

Contact

All researchers are welcome to contribute to NEPvLib. For questions, comments, hints, and contributions, please contact:

Email: Ding.Lu@uky.edu
Homepage: http://www.ms.uky.edu/~dlu245/

Acknowledgements

This website for NEPvLib is developed through work supported by the National Science Foundation under grant number DMS-2110731.