On the Computation of Null Spaces of Sparse Rectangular Matrices

Computing the null space of a sparse matrix, sometimes a rectangular 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.