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 14 articles )

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  1. Chen, Quan; Li, Jun; Yam, Chiyung; Zhang, Yu; Wong, Ngai; Chen, Guanhua: An approximate framework for quantum transport calculation with model order reduction (2015)
  2. Xia, Jianlin; Xi, Yuanzhe; Cauley, Stephen; Balakrishnan, Venkataramanan: Fast sparse selected inversion (2015)
  3. Xu, Zhenli; Maggs, A.C.: Solving fluctuation-enhanced Poisson-Boltzmann equations (2014)
  4. Benzi, Michele; Boito, Paola; Razouk, Nader: Decay properties of spectral projectors with applications to electronic structure (2013)
  5. Kalantzis, V.; Bekas, C.; Curioni, A.; Gallopoulos, E.: Accelerating data uncertainty quantification by solving linear systems with multiple right-hand sides (2013)
  6. Li, S.; Wu, W.; Darve, E.: A fast algorithm for sparse matrix computations related to inversion (2013)
  7. Stathopoulos, Andreas; Laeuchli, Jesse; Orginos, Kostas: Hierarchical probing for estimating the trace of the matrix inverse on toroidal lattices (2013)
  8. Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan: Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework. I: Total energy calculation (2012)
  9. Lin, Lin; Lu, Jianfeng; Ying, Lexing; E, Weinan: Optimized local basis set for Kohn-Sham density functional theory (2012)
  10. Li, S.; Darve, E.: Extension and optimization of the FIND algorithm: Computing Green’s and less-than Green’s functions (2012)
  11. Engquist, Björn; Ying, Lexing: Sweeping preconditioner for the Helmholtz equation: moving perfectly matched layers (2011)
  12. Lin, Lin; Yang, Chao; Lu, Jianfeng; Ying, Lexing; E, Weinan: A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2D electronic structure calculations (2011)
  13. Mahoney, Michael W.: Randomized algorithms for matrices and data (2011)
  14. Tang, Jok M.; Saad, Yousef: Domain-decomposition-type methods for computing the diagonal of a matrix inverse (2011)