Meshing genus-1 point clouds using discrete one-forms
Computers and Graphics
Uniqueness of Low-Rank Matrix Completion by Rigidity Theory
SIAM Journal on Matrix Analysis and Applications
A Fast Randomized Algorithm for Orthogonal Projection
SIAM Journal on Scientific Computing
Linear Analysis of Nonlinear Constraints for Interactive Geometric Modeling
Computer Graphics Forum
ACM Transactions on Mathematical Software (TOMS)
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Computing the null space of a sparse matrix is an important part of some computations, such as embeddings and parametrization of meshes. We propose an efficient and reliable method to compute an orthonormal basis of the null space of a sparse square or rectangular matrix (usually with more rows than columns). The main computational component in our method is a sparse $LU$ factorization with partial pivoting of the input matrix; this factorization is significantly cheaper than the $QR$ factorization used in previous methods. The paper analyzes important theoretical aspects of the new method and demonstrates experimentally that it is efficient and reliable.