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- W2113599268 abstract "In this paper, we propose a new method to efficiently compute a representation of an orthogonal basis of the nullspace of a sparse matrix operator BT with B∈Rn×m, n>m. We assume that B has full rank, i.e., rank(B)=m. It is well-known that the last n-m columns of the orthogonal matrix Q in a QR factorization B=QR form such a desired null basis. The orthogonal matrix Q can be represented either explicitly as a matrix, or implicitly as a matrix H of Householder vectors. Typically, the matrix H represents the orthogonal factor much more compactly than Q. We will employ this observation to design an efficient block algorithm that computes a sparse representation of the nullspace basis in almost optimal complexity. This new algorithm may, e.g., be used to construct a null space basis of the discrete divergence operator in the finite element context, and we will provide numerical results for this particular application." @default.
- W2113599268 created "2016-06-24" @default.
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- W2113599268 date "2008-06-01" @default.
- W2113599268 modified "2023-09-23" @default.
- W2113599268 title "Block computation and representation of a sparse nullspace basis of a rectangular matrix" @default.
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- W2113599268 doi "https://doi.org/10.1016/j.laa.2007.11.025" @default.
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