Generalized Deflated Block-Elimination

A stable algorithm is presented to solve a nonsingular bordered system of the form \begin {equation*} \begin{p matrix} A & B \\C^T & D \end{p matrix} \binom{x}{y} = \binom{f}{g},\end {equation*} where B and C are n by m matrices and the n by n matrix A could be nearly singular with at most μ...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 1986-10, Vol.23 (5), p.913-924
Main Authors: Chan, Tony F., Resasco, Diana C.
Format: Article
Language:English
Subjects:
Algorithms
Constrained optimization
Decomposition
Deflation
Exact sciences and technology
Factorization
Gaussian elimination
Mathematics
Matrices
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Optimization
Research fellowships
Sciences and techniques of general use
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Summary:A stable algorithm is presented to solve a nonsingular bordered system of the form \begin {equation*} \begin{p matrix} A & B \\C^T & D \end{p matrix} \binom{x}{y} = \binom{f}{g},\end {equation*} where B and C are n by m matrices and the n by n matrix A could be nearly singular with at most μ small singular values. The algorithm needs only a solver for A and the solution to an m + μ by m + μ dense linear system. It is, thus, well suited for problems for which A has easily exploitable structures and m + μ ≪ n, such as in continuation methods, bifurcation problems and constrained optimization.
ISSN:0036-1429
1095-7170
DOI:10.1137/0723059