Block pivoting and shortcut strategies for detecting copositivity
نویسندگان
چکیده
منابع مشابه
Strategies for Scaling and Pivoting for Sparse Symmetric Indefinite Problems
We consider ways of implementing preordering and scaling for symmetric systems and show the effect of using this technique with a multifrontal code for sparse symmetric indefinite systems. After having presented a new method for scaling, we propose a way of using an approximation to a symmetric weighted matching to predefine 1×1 and 2×2 pivots prior to the ordering and analysis phase. We also p...
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Solving large linear systems is a fundamental task in many interesting problems, including finite element methods (FEM) or (non-)linear least squares (NLS) for inference in graphical models such as simultaneous localization and mapping (SLAM) in robotics or bundle adjustment (BA) in computer vision. Furthermore, the problems of interest here are sparse. The most time-consuming parts are sparse ...
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The performance of a sparse direct solver is dependent upon the pivot sequence that is chosen during the analyse phase. In the case of symmetric indefinite systems, it may be necessary to modify this sequence during the factorization to ensure numerical stability. Delaying pivots can have serious consequences in terms of time as well as the memory and flops required for the factorization and su...
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متن کاملPreprint : Considering Copositivity Locally ∗
We say that a symmetric matrix A is copositive if vTAv ≥ 0 for all nonnegative vectors v. The main result of this paper is a characterization of the cone of feasible directions at a copositive matrix A, i.e., the convex cone of symmetric matrices B such that there exists δ > 0 satisfying A + δB being copositive. This cone is described by a set of linear inequalities on the elements of B constru...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1996
ISSN: 0024-3795
DOI: 10.1016/0024-3795(95)00165-4