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 44 articles , 1 standard article )

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  1. Ito, Shinji; Nakatsukasa, Yuji: Stable polefinding and rational least-squares fitting via eigenvalues (2018)
  2. Kalantzis, Vassilis; Xi, Yuanzhe; Saad, Yousef: Beyond automated multilevel substructuring: domain decomposition with rational filtering (2018)
  3. Krämer, Lukas; Lang, Bruno: Convergence of integration-based methods for the solution of standard and generalized Hermitian eigenvalue problems (2018)
  4. Xiao, Jinyou; Wang, Junpeng; Liang, Tengfei; Wen, Lihua: The RSRR method for solving large-scale nonlinear eigenvalue problems in boundary element method (2018)
  5. Zheng, Chang-Jun; Bi, Chuan-Xing; Zhang, Chuanzeng; Gao, Hai-Feng; Chen, Hai-Bo: Free vibration analysis of elastic structures submerged in an infinite or semi-infinite fluid domain by means of a coupled FE-BE solver (2018)
  6. Aishima, Kensuke: On convergence of iterative projection methods for symmetric eigenvalue problems (2017)
  7. Barkatou, Moulay; Boito, Paola; Segura Ugalde, Esteban: A contour integral approach to the computation of invariant pairs (2017)
  8. Beckermann, Bernhard; Townsend, Alex: On the singular values of matrices with displacement structure (2017)
  9. Bini, Dario A.; Massei, Stefano; Robol, Leonardo: On the decay of the off-diagonal singular values in cyclic reduction (2017)
  10. Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail: Multiscale S-fraction reduced-order models for massive wavefield simulations (2017)
  11. Imakura, Akira; Sakurai, Tetsuya: Block Krylov-type complex moment-based eigensolvers for solving generalized eigenvalue problems (2017)
  12. Lin, Lin: Localized spectrum slicing (2017)
  13. Lin, Lin: Randomized estimation of spectral densities of large matrices made accurate (2017)
  14. Lu, Jianfeng; Yang, Haizhao: Preconditioning orbital minimization method for planewave discretization (2017)
  15. Misawa, Ryota; Niino, Kazuki; Nishimura, Naoshi: Boundary integral equations for calculating complex eigenvalues of transmission problems (2017)
  16. Xiao, Jinyou; Zhang, Chuanzeng; Huang, Tsung-Ming; Sakurai, Tetsuya: Solving large-scale nonlinear eigenvalue problems by rational interpolation and resolvent sampling based Rayleigh-Ritz method (2017)
  17. Xiao, Jinyou; Zhou, Hang; Zhang, Chuanzeng; Xu, Chao: Solving large-scale finite element nonlinear eigenvalue problems by resolvent sampling based Rayleigh-Ritz method (2017)
  18. Xi, Yuanzhe; Saad, Yousef: A rational function preconditioner for indefinite sparse linear systems (2017)
  19. Ye, Xin; Xia, Jianlin; Chan, Raymond H.; Cauley, Stephen; Balakrishnan, Venkataramanan: A fast contour-integral eigensolver for non-Hermitian matrices (2017)
  20. Zheng, C. J.; Zhang, C.; Bi, C. X.; Gao, H. F.; Du, L.; Chen, H. B.: Coupled FE-BE method for eigenvalue analysis of elastic structures submerged in an infinite fluid domain (2017)

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