The FEAST solver package is a free high-performance numerical library for solving the standard or generalized eigenvalue problem, and obtaining all the eigenvalues and eigenvectors within a given search interval. It is based on an innovative fast and stable numerical algorithm -- named the FEAST algorithm -- which deviates fundamentally from the traditional Krylov subspace iteration based techniques (Arnoldi and Lanczos algorithms) or other Davidson-Jacobi techniques. The FEAST algorithm takes its inspiration from the density-matrix representation and contour integration technique in quantum mechanics. It is free from explicit orthogonalization procedures, and its main computational tasks consist of solving very few inner independent linear systems with multiple right-hand sides and one reduced eigenvalue problem orders of magnitude smaller than the original one. The FEAST algorithm combines simplicity and efficiency and offers many important capabilities for achieving high performance, robustness, accuracy, and scalability on parallel architectures. This general purpose FEAST solver package includes both reverse communication interfaces and ready to use predefined interfaces for dense, banded and sparse systems. It includes double and single precision arithmetic, and all the interfaces are compatible with Fortran (77,90) and C. FEAST is both a comprehensive library package, and an easy to use software. This solver is expected to significantly augment numerical performances and capabilities in large-scale modern applications.

References in zbMATH (referenced in 23 articles , 1 standard article )

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  1. Lin, Lin: Randomized estimation of spectral densities of large matrices made accurate (2017)
  2. Lin, Lin: Localized spectrum slicing (2017)
  3. Graen, Timo; Grubmüller, Helmut: NuSol -- numerical solver for the 3D stationary nuclear Schrödinger equation (2016)
  4. Imakura, Akira; Du, Lei; Sakurai, Tetsuya: Error bounds of Rayleigh-Ritz type contour integral-based eigensolver for solving generalized eigenvalue problems (2016)
  5. Kestyn, James; Polizzi, Eric; Tang, Ping Tak Peter: Feast eigensolver for non-Hermitian problems (2016)
  6. Li, Ruipeng; Xi, Yuanzhe; Vecharynski, Eugene; Yang, Chao; Saad, Yousef: A thick-restart Lanczos algorithm with polynomial filtering for Hermitian eigenvalue problems (2016)
  7. Nakatsukasa, Yuji; Freund, Roland W.: Computing fundamental matrix decompositions accurately via the matrix sign function in two iterations: the power of Zolotarev’s functions (2016)
  8. Rashedi, Somaiyeh; Ebadi, Ghodrat; Birk, Sebastian; Frommer, Andreas: On short recurrence Krylov type methods for linear systems with many right-hand sides (2016)
  9. Van Barel, Marc: Designing rational filter functions for solving eigenvalue problems by contour integration (2016)
  10. Van Barel, Marc; Kravanja, Peter: Nonlinear eigenvalue problems and contour integrals (2016)
  11. Vecharynski, Eugene: A generalization of Saad’s bound on harmonic Ritz vectors of Hermitian matrices (2016)
  12. Xi, Yuanzhe; Saad, Yousef: Computing partial spectra with least-squares rational filters (2016)
  13. Zeng, Fang; Sun, JiGuang; Xu, LiWei: A spectral projection method for transmission eigenvalues (2016)
  14. Zheng, Chang-Jun; Gao, Hai-Feng; Du, Lei; Chen, Hai-Bo; Zhang, Chuanzeng: An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method (2016)
  15. Austin, Anthony P.; Trefethen, Lloyd N.: Computing eigenvalues of real symmetric matrices with rational filters in real arithmetic (2015)
  16. Güttel, Stefan; Polizzi, Eric; Tang, Ping Tak Peter; Viaud, Gautier: Zolotarev quadrature rules and load balancing for the FEAST eigensolver (2015)
  17. Liu, Xin; Wen, Zaiwen; Zhang, Yin: An efficient Gauss-Newton algorithm for symmetric low-rank product matrix approximations (2015)
  18. Röhrig-Zöllner, Melven; Thies, Jonas; Kreutzer, Moritz; Alvermann, Andreas; Pieper, Andreas; Basermann, Achim; Hager, Georg; Wellein, Gerhard; Fehske, Holger: Increasing the performance of the Jacobi-Davidson method by blocking (2015)
  19. Jerome, Joseph W.; Polizzi, Eric: Discretization of time-dependent quantum systems: real-time propagation of the evolution operator (2014)
  20. Tang, Ping Tak Peter; Polizzi, Eric: FEAST as a subspace iteration eigensolver accelerated by approximate spectral projection (2014)

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Further publications can be found at: http://www.ecs.umass.edu/~polizzi/feast/references.htm