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)
The role of elimination trees in sparse factorization
SIAM Journal on Matrix Analysis and Applications
Path-following methods for linear programming
SIAM Review
Sparse matrices in matlab: design and implementation
SIAM Journal on Matrix Analysis and Applications
Sparse QR factorization in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Parallel sparse QR factorization on shared memory architectures
Parallel Computing
Parallel Sparse Orthogonal Factorization on Distributed-Memory Multiprocessors
SIAM Journal on Scientific Computing
Multifrontal Computation with the Orthogonal Factors of Sparse Matrices
SIAM Journal on Matrix Analysis and Applications
LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
ACM Transactions on Mathematical Software (TOMS)
The Multifrontal Solution of Indefinite Sparse Symmetric Linear
ACM Transactions on Mathematical Software (TOMS)
A software package for sparse orthogonal factorization and updating
ACM Transactions on Mathematical Software (TOMS)
Cache efficiency and scalability on multi-core architectures
PaCT'11 Proceedings of the 11th international conference on Parallel computing technologies
A direct orthogonal sparse static methodology for a finite continuation hybrid LP solver
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
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Numerical and computational aspects of direct methods for largeand sparseleast squares problems are considered. After a brief survey of the most oftenused methods, we summarize the important conclusions made from anumerical comparison in matlab. Significantly improved algorithms haveduring the last 10-15 years made sparse QR factorization attractive, andcompetitive to previously recommended alternatives. Of particular importanceis the multifrontal approach, characterized by low fill-in, dense subproblemsand naturally implemented parallelism. We describe a Householder multifrontalscheme and its implementation on sequential and parallel computers. Availablesoftware has in practice a great influence on the choice of numericalalgorithms. Less appropriate algorithms are thus often used solely because ofexisting software packages. We briefly survey softwarepackages for the solution of sparse linear least squares problems. Finally,we focus on various applications from optimization, leading to the solution oflarge and sparse linear least squares problems. In particular, we concentrateon the important case where the coefficient matrix is a fixed general sparsematrix with a variable diagonal matrix below. Inner point methods forconstrained linear least squares problems give, for example, rise to suchsubproblems. Important gains can be made by taking advantage of structure.Closely related is also the choice of numerical method for these subproblems.We discuss why the less accurate normal equations tend to be sufficient inmany applications.