Shift-and-Invert Parallel spectral transformations eigensolver

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SIPs is a parallel sparse eigensolver for real and symmetric generalized eigenvalue problems. Motivated by quantum chemistry and material science applications, where a large portion of eigensolutions are required, SIPs was initially developed in 2007.1 SIPs solves the eigenvalue problem with distributed spectrum slicing method and it is built on top of PETSc and SLEPc libraries. Thanks to improvements in the robustness and efficiency of the underlying mathematical libraries,2 a later implementation of SIPs demonstrated scalability of the eigensolver beyond 200,000 cores for matrices with more than 500,000 rows.3 A more recent implementation of SIPs is now available in SLEPc package and it is integrated into a branch of SIESTA, an initio molecular dynamics package. ELSI developers also provide an interface to SIPs eigensolver and other solvers for quantum chemistry applications.


  1. Zhang, H.; Smith, B.; Sternberg, M.; Zapol, P.
    SIPs: Shift-and-Invert Parallel Spectral Transformations.
    ACM Trans. Math. Softw. 2007, 33, 9–es. DOI=10.1145/1236463.1236464
  2. Campos, C.; Román, J. E.
    Strategies for Spectrum Slicing Based on Restarted Lanczos Methods.
    Numer. Algorithms 2012, 60, 279–295. DOI=10.1007/s11075-012-9564-z
  3. Keçeli, M.; Zhang, H.; Zapol, P.; Dixon, D. A.; Wagner, A. F.
    Shift-and-Invert Parallel Spectral Transformation Eigensolver: Massively Parallel Performance for Density-Functional Based Tight-Binding.
    J. Comput. Chem. 2016, 37, 448–459. DOI=10.1002/jcc.24254
  4. Keçeli M.; Corsetti F.; Campos C.; Román, J. E.; Vázquez-Mayagoitia Á; Zhang, H.; Zapol, P.; & Wagner A, F.
    SIESTA-SIPs: Massively parallel spectrum-slicing eigensolver for an ab initio molecular dynamics package. (under review, 2018)