A compact row storage scheme for Cholesky factors using elimination trees
ACM Transactions on Mathematical Software (TOMS)
Updating the inverse of a matrix
SIAM Review
A set of level 3 basic linear algebra subprograms
ACM Transactions on Mathematical Software (TOMS)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
ACM Transactions on Mathematical Software (TOMS)
A Cholesky up- and downdating algorithm for systolic and SIMD architectures
SIAM Journal on Scientific Computing
On finding supernodes for sparse matrix computations
SIAM Journal on Matrix Analysis and Applications
Block sparse Cholesky algorithms on advanced uniprocessor computers
SIAM Journal on Scientific Computing
An Efficient Algorithm to Compute Row and Column Counts for Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
Modifying a Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
LAPACK Users' guide (third ed.)
LAPACK Users' guide (third ed.)
Basic Linear Algebra Subprograms for Fortran Usage
ACM Transactions on Mathematical Software (TOMS)
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
Corrigenda: “An Extended Set of FORTRAN Basic Linear Algebra Subprograms”
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
Multiple-Rank Modifications of a Sparse Cholesky Factorization
SIAM Journal on Matrix Analysis and Applications
PASTIX: a high-performance parallel direct solver for sparse symmetric positive definite systems
Parallel Computing - Parallel matrix algorithms and applications
The design and implementation of a new out-of-core sparse cholesky factorization method
ACM Transactions on Mathematical Software (TOMS)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
Direct Methods for Sparse Linear Systems (Fundamentals of Algorithms 2)
ACM Transactions on Mathematical Software (TOMS)
Experiences of sparse direct symmetric solvers
ACM Transactions on Mathematical Software (TOMS)
A sparse proximal implementation of the LP dual active set algorithm
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Technical Section: Dynamic harmonic fields for surface processing
Computers and Graphics
Fast recovery of weakly textured surfaces from monocular image sequences
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part IV
SMI 2011: Full Paper: Template-based quadrilateral meshing
Computers and Graphics
SMI 2011: Full Paper: A topology-preserving optimization algorithm for polycube mapping
Computers and Graphics
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
Updated sparse cholesky factors for corotational elastodynamics
ACM Transactions on Graphics (TOG)
A Gauss-Newton Method for the Integration of Spatial Normal Fields in Shape Space
Journal of Mathematical Imaging and Vision
Computers & Mathematics with Applications
Saddle vertex graph (SVG): a novel solution to the discrete geodesic problem
ACM Transactions on Graphics (TOG)
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The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of L does not change, it is not suitable for methods that modify a sparse Cholesky factorization after a low-rank change to A (an update/downdate, Ā = A ± WWT). Supernodes merge and split apart during an update/downdate. Dynamic supernodes are introduced which allow a sparse Cholesky update/downdate to obtain performance competitive with conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional (BLAS-based) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse Cholesky factorization and update/downdate package which forms the basis of x = A\b MATLAB when A is sparse and symmetric positive definite.