SelInv --- An Algorithm for Selected Inversion of a Sparse Symmetric Matrix. We describe an efficient implementation of an algorithm for computing selected elements of a general sparse symmetric matrix A that can be decomposed as A = LDLT, where L is lower triangular and D is diagonal. Our implementation, which is called SelInv, is built on top of an efficient supernodal left-looking LDLT factorization of A. We discuss how computational efficiency can be gained by making use of a relative index array to handle indirect addressing. We report the performance of SelInv on a collection of sparse matrices of various sizes and nonzero structures. We also demonstrate how SelInv can be used in electronic structure calculations.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 30 articles )

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  1. Harbrecht, Helmut; Multerer, Michael: A fast direct solver for nonlocal operators in wavelet coordinates (2021)
  2. Lin, Lin; Wu, Xiaojie: Numerical solution of large scale Hartree-Fock-Bogoliubov equations (2021)
  3. Schäfer, Florian; Sullivan, T. J.; Owhadi, Houman: Compression, inversion, and approximate PCA of dense kernel matrices at near-linear computational complexity (2021)
  4. Liu, Xiao; Xia, Jianlin; de Hoop, Maarten: Fast factorization update for general elliptic equations under multiple coefficient updates (2020)
  5. Polizzi, Eric; Saad, Yousef: Computational materials science and engineering (2020)
  6. Bollhöfer, Matthias; Eftekhari, Aryan; Scheidegger, Simon; Schenk, Olaf: Large-scale sparse inverse covariance matrix estimation (2019)
  7. Lin, Lin; Lu, Jianfeng; Ying, Lexing: Numerical methods for Kohn-Sham density functional theory (2019)
  8. Liu, Pei; Ji, Xia; Xu, Zhenli: Modified Poisson-Nernst-Planck model with accurate Coulomb correlation in variable media (2018)
  9. Li, Xiantao; Lin, Lin; Lu, Jianfeng: PEXSI-(\Sigma): a Green’s function embedding method for Kohn-Sham density functional theory (2018)
  10. Sidén, Per; Lindgren, Finn; Bolin, David; Villani, Mattias: Efficient covariance approximations for large sparse precision matrices (2018)
  11. Khoromskaia, Venera; Khoromskij, Boris N.: Block circulant and Toeplitz structures in the linearized Hartree-Fock equation on finite lattices: tensor approach (2017)
  12. Liu, Pei; Ma, Manman; Xu, Zhenli: Understanding depletion induced like-charge attraction from self-consistent field model (2017)
  13. Stachurski, Andrzej: On a conjugate directions method for solving strictly convex QP problem (2017)
  14. Wu, Lingfei; Laeuchli, Jesse; Kalantzis, Vassilis; Stathopoulos, Andreas; Gallopoulos, Efstratios: Estimating the trace of the matrix inverse by interpolating from the diagonal of an approximate inverse (2016)
  15. Chen, Quan; Li, Jun; Yam, Chiyung; Zhang, Yu; Wong, Ngai; Chen, Guanhua: An approximate framework for quantum transport calculation with model order reduction (2015)
  16. Xia, Jianlin; Xi, Yuanzhe; Cauley, Stephen; Balakrishnan, Venkataramanan: Fast sparse selected inversion (2015)
  17. Xu, Zhenli; Maggs, A. C.: Solving fluctuation-enhanced Poisson-Boltzmann equations (2014)
  18. Benzi, Michele; Boito, Paola; Razouk, Nader: Decay properties of spectral projectors with applications to electronic structure (2013)
  19. Hetmaniuk, U.; Zhao, Y.; Anantram, M. P.: A nested dissection approach to modeling transport in nanodevices: algorithms and applications (2013)
  20. Kalantzis, V.; Bekas, C.; Curioni, A.; Gallopoulos, E.: Accelerating data uncertainty quantification by solving linear systems with multiple right-hand sides (2013)

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