FEAST

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 74 articles , 1 standard article )

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  1. Gopalakrishnan, Jay; Grubišić, Luka; Ovall, Jeffrey: Spectral discretization errors in filtered subspace iteration (2020)
  2. Horning, Andrew; Townsend, Alex: FEAST for differential eigenvalue problems (2020)
  3. Liu, Xiao; Xi, Yuanzhe; Saad, Yousef; de Hoop, Maarten V.: Solving the three-dimensional high-frequency Helmholtz equation using contour integration and polynomial preconditioning (2020)
  4. Shen, Chungen; Fan, Changxing; Wang, Yunlong; Xue, Wenjuan: Limited memory BFGS algorithm for the matrix approximation problem in Frobenius norm (2020)
  5. Toth, Florian; Kaltenbacher, Manfred: Coupling of incompressible free-surface flow, acoustic fluid and flexible structure via a modal basis (2020)
  6. Alvermann, Andreas; Basermann, Achim; Bungartz, Hans-Joachim; Carbogno, Christian; Ernst, Dominik; Fehske, Holger; Futamura, Yasunori; Galgon, Martin; Hager, Georg; Huber, Sarah; Huckle, Thomas; Ida, Akihiro; Imakura, Akira; Kawai, Masatoshi; Köcher, Simone; Kreutzer, Moritz; Kus, Pavel; Lang, Bruno; Lederer, Hermann; Manin, Valeriy; Marek, Andreas; Nakajima, Kengo; Nemec, Lydia; Reuter, Karsten; Rippl, Michael; Röhrig-Zöllner, Melven; Sakurai, Tetsuya; Scheffler, Matthias; Scheurer, Christoph; Shahzad, Faisal; Simoes Brambila, Danilo; Thies, Jonas; Wellein, Gerhard: Benefits from using mixed precision computations in the ELPA-AEO and ESSEX-II eigensolver projects (2019)
  7. Beckermann, Bernhard; Townsend, Alex: Bounds on the singular values of matrices with displacement structure (2019)
  8. Camps, Daan; Meerbergen, Karl; Vandebril, Raf: A rational QZ method (2019)
  9. Elsworth, Steven; Güttel, Stefan: Conversions between barycentric, RKFUN, and Newton representations of rational interpolants (2019)
  10. Gawlik, Evan S.: Zolotarev iterations for the Matrix square Root (2019)
  11. Gopalakrishnan, Jay; Grubišić, Luka; Ovall, Jeffrey; Parker, Benjamin: Analysis of FEAST spectral approximations using the DPG discretization (2019)
  12. Hoshi, Takeo; Imachi, Hiroto; Kuwata, Akiyoshi; Kakuda, Kohsuke; Fujita, Takatoshi; Matsui, Hiroyuki: Numerical aspect of large-scale electronic state calculation for flexible device material (2019)
  13. Lin, Lin; Lu, Jianfeng; Ying, Lexing: Numerical methods for Kohn-Sham density functional theory (2019)
  14. Li, Ruipeng; Xi, Yuanzhe; Erlandson, Lucas; Saad, Yousef: The eigenvalues slicing library (EVSL): algorithms, implementation, and software (2019)
  15. Liu, J.; Sun, J.; Turner, T.: Spectral indicator method for a non-selfadjoint Steklov eigenvalue problem (2019)
  16. Li, Yingzhou; Lin, Lin: Globally constructed adaptive local basis set for spectral projectors of second order differential operators (2019)
  17. Manguoğlu, Murat; Mehrmann, Volker: A robust iterative scheme for symmetric indefinite systems (2019)
  18. Murakami, Hiroshi: Filters consist of a few resolvents to solve real symmetric definite generalized eigenproblems (2019)
  19. Saibaba, Arvind K.: Randomized subspace iteration: analysis of canonical angles and unitarily invariant norms (2019)
  20. Yin, Guojian: A contour-integral based method for counting the eigenvalues inside a region (2019)

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