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

Authors:
Lin Lin;Chao Yang;Juan C. Meza;Jianfeng Lu;Lexing Ying;Weinan E
Affiliations:
Princeton University;Lawrence Berkeley National Laboratory;Lawrence Berkeley National Laboratory;Courant Institute of Mathematical Sciences;University of Texas at Austin;Princeton University
Venue:
ACM Transactions on Mathematical Software (TOMS)
Year:
2011

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Abstract

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.