Predicting fill for sparse orthogonal factorization
Journal of the ACM (JACM)
On general row merging schemes for sparse given transformations
SIAM Journal on Scientific and Statistical Computing
ACM Transactions on Mathematical Software (TOMS)
Computing the block triangular form of a sparse matrix
ACM Transactions on Mathematical Software (TOMS)
Sparse matrices in matlab: design and implementation
SIAM Journal on Matrix Analysis and Applications
A New Implementation of Sparse Gaussian Elimination
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
Sparse Linear Least Squares Problems in Optimization
Computational Optimization and Applications
A column pre-ordering strategy for the unsymmetric-pattern multifrontal method
ACM Transactions on Mathematical Software (TOMS)
Square Root SAM: Simultaneous Localization and Mapping via Square Root Information Smoothing
International Journal of Robotics Research
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 3
A stable primal---dual approach for linear programming under nondegeneracy assumptions
Computational Optimization and Applications
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
An efficient algorithm for sparse null space basis problem using ABS methods
Numerical Algorithms
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In the recently presented sparse matrix extension of MATLAB, there is no routine for sparse QR factorization. Sparse linear least-squares problems are instead solved by the augmented system method. The accuracy in computed solutions is strongly dependent on a scaling parameter &dgr;. Its optimal value is expensive to compute, and it must therefore be approximated by a simple heuristic. We describe a multifrontal method for sparse QR factorization and its implementation in MATLAB. It is well known that the multifrontal approach is suitable for vector machines. We show that it is also attractive in MATLAB. In both cases, scalar operations are expensive, and the reformulation of the sparse problem into dense subproblems is advantageous. Using the new routine, we implement two methods for the solution of sparse linear least-squares problems and compare these with the built-in MATLAB function. We show that the QR-based methods normally are much faster and more accurate than the MATLAB implementation of the augmented system method. A better choice of the parameter &dgr; or iterative refinement must be used to make the augmented system method as accurate as the methods based on QR factorization.