2004/06/01 by Timothy A. Davis · 1,412 citations
Computer Science · Engineering · #Algorithm #Computational science #Computer science #Data structure #Factorization #Incomplete Cholesky factorization #Incomplete LU factorization #LU decomposition #MATLAB #Matrix (chemical analysis) #Matrix Theory and Algorithms #Matrix decomposition #Parallel Computing and Optimization Techniques #Parallel computing #Programming language #Simple (philosophy) #Sparse matrix #Theoretical computer science #VLSI and FPGA Design Techniques
paper · doi:10.1145/992200.992206
published in ACM Transactions on Mathematical Software 30(2), 196-199 (Association for Computing Machinery)
openalex publication_date 2004/06/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/04
An ANSI C code for sparse LU factorization is presented that combines a 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 fill-in, work, and memory usage during the subsequent numerical factorization. User-callable routines are provided for ordering and analyzing 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 complex 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. UMFPACK is incorporated as a built-in operator in MATLAB 6.5 as x = A\b when A is sparse and unsymmetric.