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Persistent URL http://purl.org/net/epubs/work/63059
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Record Id 63059
Title Orderings governed by numerical factorization
Abstract We study the solution of sparse least-squares problems using an augmented system approach: $$ \left ({ \begin{array} {ll} I & A \\ A^T & 0 \end{array} } \right ) \left ({ \begin{array} {c} r \\ x \end{array} } \right ) ~=~ \left ({ \begin{array} {c} b \\ 0 \end{array} } \right ) $$ If the null space approach for constrained optimization is used, a crucial aspect is the selection of the basis rows from the overdetermined matrix $A$. We discuss the effect of this showing that the concept of condition number and conditioning needs to be rethought in this case. We illustrate our discussion with runs using a basis selection routine from HSL that involves a sparse factorization with rook pivoting and a subsequent solution of the augmented system using iterative methods.
Organisation CSE-NAG , STFC , SCI-COMP
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Language English (EN)
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Presentation Presented at SIAM Conference on Applied Linear Algebra, Valencia, Spain, 17-22 Jun 2012. valencia_isd.pdf 2012
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