The Dual Active Set Algorithm and Its Application to Linear Programming
Computational Optimization and Applications
A software package for sparse orthogonal factorization and updating
ACM Transactions on Mathematical Software (TOMS)
Primal-Dual Strategy for State-Constrained Optimal Control Problems
Computational Optimization and Applications
Scalable Sparse Matrix Techniques for Modeling Crack Growth
PARA '02 Proceedings of the 6th International Conference on Applied Parallel Computing Advanced Scientific Computing
Geometry-Aware Bases for Shape Approximation
IEEE Transactions on Visualization and Computer Graphics
ACM Transactions on Mathematical Software (TOMS)
Experiences of sparse direct symmetric solvers
ACM Transactions on Mathematical Software (TOMS)
Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing
International Journal of Robotics Research
Design of tangent vector fields
ACM SIGGRAPH 2007 papers
SBIM '07 Proceedings of the 4th Eurographics workshop on Sketch-based interfaces and modeling
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate
ACM Transactions on Mathematical Software (TOMS)
Efficient representation and analysis of power grids
Proceedings of the conference on Design, automation and test in Europe
Dynamic Supernodes in Sparse Cholesky Update/Downdate and Triangular Solves
ACM Transactions on Mathematical Software (TOMS)
Technical Section: Dynamic harmonic fields for surface processing
Computers and Graphics
Feature-aligned shape texturing
ACM SIGGRAPH Asia 2009 papers
Efficient simulation of power grids
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems - Special section on the ACM IEEE international conference on formal methods and models for codesign (MEMOCODE) 2009
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)
Can Mean-Curvature Flow be Modified to be Non-singular?
Computer Graphics Forum
Parameter estimation in high dimensional Gaussian distributions
Statistics and Computing
Classification of brain activation via spatial Bayesian variable selection in fMRI regression
Advances in Data Analysis and Classification
Hi-index | 0.00 |
Given a sparse symmetric positive definite matrix ${\bf AA}^{\sf T}$ and an associated sparse Cholesky factorization ${\bf LDL}^{\sf T}$ or ${\bf LL}^{\sf T}$, we develop sparse techniques for obtaining the new factorization associated with either adding a column to ${\bf A}$ or deleting a column from ${\bf A}$. Our techniques are based on an analysis and manipulation of the underlying graph structure and on ideas of Gill et al.\ [ Math. Comp., 28 (1974), pp. 505--535] for modifying a dense Cholesky factorization. We show that our methods extend to the general case where an arbitrary sparse symmetric positive definite matrix is modified. Our methods are optimal in the sense that they take time proportional to the number of nonzero entries in ${\bf L}$ and ${\bf D}$ that change.