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 90 articles , 1 standard article )

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  1. Horning, Andrew; Nakatsukasa, Yuji: Twice is enough for dangerous eigenvalues (2022)
  2. Betz, F., Binkowski, F., Burger, S.: RPExpand: Software for Riesz projection expansion of resonance phenomena (2021) not zbMATH
  3. Campos, Carmen; Roman, Jose E.: NEP. A module for the parallel solution of nonlinear eigenvalue problems in SLEPc (2021)
  4. Kalantzis, Vassilis; Xi, Yuanzhe; Horesh, Lior: Fast randomized non-Hermitian eigensolvers based on rational filtering and matrix partitioning (2021)
  5. Kollnig, Konrad; Bientinesi, Paolo; Di Napoli, Edoardo A.: Rational spectral filters with optimal convergence rate (2021)
  6. Lorin, Emmanuel; Tian, Simon: A numerical study of fractional linear algebraic systems (2021)
  7. Miao, Cun-Qiang; Wu, Wen-Ting: On relaxed filtered Krylov subspace method for non-symmetric eigenvalue problems (2021)
  8. Morikuni, Keiichi: Projection method for eigenvalue problems of linear nonsquare matrix pencils (2021)
  9. Carcenac, Manuel; Redif, Soydan: Application of the sequential matrix diagonalization algorithm to high-dimensional functional MRI data (2020)
  10. Ezvan, Olivier; Zeng, Xiaoshu; Ghanem, Roger; Gencturk, Bora: Multiscale modal analysis of fully-loaded spent nuclear fuel canisters (2020)
  11. Gopalakrishnan, Jay; Grubišić, Luka; Ovall, Jeffrey: Spectral discretization errors in filtered subspace iteration (2020)
  12. Horning, Andrew; Townsend, Alex: FEAST for differential eigenvalue problems (2020)
  13. Lieder, Felix: Solving large-scale cubic regularization by a generalized eigenvalue problem (2020)
  14. 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)
  15. Miao, Cun-Qiang: On Chebyshev-Davidson method for symmetric generalized eigenvalue problems (2020)
  16. Polizzi, Eric; Saad, Yousef: Computational materials science and engineering (2020)
  17. Shen, Chungen; Fan, Changxing; Wang, Yunlong; Xue, Wenjuan: Limited memory BFGS algorithm for the matrix approximation problem in Frobenius norm (2020)
  18. Toth, Florian; Kaltenbacher, Manfred: Coupling of incompressible free-surface flow, acoustic fluid and flexible structure via a modal basis (2020)
  19. Ye, Xin; Xia, Jianlin; Ying, Lexing: Analytical low-rank compression via proxy point selection (2020)
  20. 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)

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