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SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix

TOM00051 ACM (Typeset by SPi, Manila, Philippines) 1 of 19 February 24, 2011 SelInv ”An Algorithm for Selected Inversion of a Sparse Symmetric Matrix LIN LIN, Princeton University CHAO YANG and JUAN C. MEZA, Lawrence Berkeley National Laboratory JIANFENG LU, Courant Institute of Mathematical Sciences LEXING YING, University of Texas at Austin WEINAN E, Princeton University We describe an ef cient implementation of an algorithm for computing selected elements of a general sparse symmetric matrix A that can be decomposed as A = L D L T , where L is lower triangular and D is diagonal. Our implementation, which is called SelInv, is built on top of an ef cient supernodal left-looking L D L T factorization of A. We discuss how computational ef ciency 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. Categories and Subject Descriptors: G.4 [Mathematical Software]: ”Algorithm design and analysis; I.1.2 [Symbolic and Algebraic Manipulation]: Algorithms ”Algebraic algorithms General Terms: Design, Performance Additional Key Words and http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Mathematical Software (TOMS) Association for Computing Machinery

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