SelInv - An algorithm for selected inversion of a sparse symmetric matrix

Lin Lin, Chao Yang, Juan C. Meza, Jianfeng Lu, Lexing Ying, E. Weinan

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73 Scopus citations


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.

Original languageEnglish (US)
Article number40
JournalACM Transactions on Mathematical Software
Issue number4
StatePublished - Feb 2011

All Science Journal Classification (ASJC) codes

  • Software
  • Applied Mathematics


  • Electronic structure calculation
  • Elimination tree
  • Selected inversion
  • Sparse LDL factorization
  • Supernodes


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