Hybrid methods for large sparse nonlinear least squares |
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Authors: | L Luk?an |
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Institution: | (1) Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic |
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Abstract: | Hybrid methods are developed for improving the Gauss-Newton method in the case of large residual or ill-conditioned nonlinear least-square problems. These methods are used usually in a form suitable for dense problems. But some standard approaches are unsuitable, and some new possibilities appear in the sparse case. We propose efficient hybrid methods for various representations of the sparse problems. After describing the basic ideas that help deriving new hybrid methods, we are concerned with designing hybrid methods for sparse Jacobian and sparse Hessian representations of the least-square problems. The efficiency of hybrid methods is demonstrated by extensive numerical experiments.This work was supported by the Czech Republic Grant Agency, Grant 201/93/0129. The author is indebted to Jan Vlek for his comments on the first draft of this paper and to anonymous referees for many useful remarks. |
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Keywords: | Unconstrained optimization nonlinear least squares line search methods trust region methods Gauss-Newton method hybrid methods sparse problems matrix iterative methods matrix direct methods computational experiments |
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