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Algorithm 8xx : UMFPACK V3.2, an unsymmetric-pattern multifrontal method with a column pre-ordering strategy

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Department of Computer and Information Science and Engineering, University of Florida
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  • Computer Science

Abstract

Algorithm 8xx: UMFPACK V3.2, an unsymmetric-pattern multifrontal method with a column pre-ordering strategy � Timothy A. Davis y January 2, 2002 Technical report TR-02-002. Department of Computer and Information Science and Engineering, University of Florida. Abstract An ANSI C code for sparse LU factorization is presented that com- bines a left-looking column pre-ordering strategy with a right-looking unsymmetric-pattern multifrontal numerical factorization. The pre- ordering and symbolic analysis phase computes an upper bound on �ll-in, work, and memory usage during the subsequent numerical fac- torization. User-callable routines are provided for ordering and ana- lyzing a sparse matrix, computing the numerical factorization, solving a system with the LU factors, transposing and permuting a sparse matrix, and converting between sparse matrix representations. The simple user interface shields the user from the details of the com- plex sparse factorization data structures by returning simple handles to opaque objects. Additional user-callable routines are provided for printing and extracting the contents of these opaque objects. An even simpler way to use the package is through its MATLAB interface. A future version of MATLAB will incorporate UMFPACK as its default sparse matrix factorization method. � This work was supported by the National Science Foundation, under grants DMS- 9504974 and DMS-9803599. y Dept. of Computer and Information Science and Engineering, Univ. of Florida, Gainesville, FL, USA. email: [email protected] .edu. http://www.cise.u .edu/�davis. 1 Categories and Subject Descriptors: G.1.3 [Numerical Analysis]: Numer- ical Linear Algebra { linear systems (direct methods), sparse and very large systems G.4 [Mathematics of Computing]: Mathematical Software { algo- rithm analysis, eÆciency General terms: Algorithms, Experimentation, Performance. Keywords: sparse nonsymmetric matrices, linear equations, multifr

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