Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
On Algorithms for Obtaining a Maximum Transversal
ACM Transactions on Mathematical Software (TOMS)
Computer Solution of Large Sparse Positive Definite
Computer Solution of Large Sparse Positive Definite
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
Sparse QR factorization in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Sparse Linear Least Squares Problems in Optimization
Computational Optimization and Applications
A software package for sparse orthogonal factorization and updating
ACM Transactions on Mathematical Software (TOMS)
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
A column approximate minimum degree ordering algorithm
ACM Transactions on Mathematical Software (TOMS)
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
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In solving large sparse linear least squares problems A x ≃ b, several different numeric methods involve computing the same upper triangular factor R of A. It is of interest to be able to compute the nonzero structure of R, given only the structure of A. The solution to this problem comes from the theory of matchings in bipartite graphs. The structure of A is modeled with a bipartite graph, and it is shown how the rows and columns of A can be rearranged into a structure from which the structure of its upper triangular factor can be correctly computed. Also, a new method for solving sparse least squares problems, called block back-substitution, is presented. This method assures that no unnecessary space is allocated for fill, and that no unnecessary space is needed for intermediate fill.