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arXiv · 1610.03095

Greedy Gauss-Newton algorithm for finding sparse solutions to nonlinear underdetermined systems of equations

Mårten Gulliksson·Anna Oleynik
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Abstract

We consider the problem of finding sparse solutions to a system of underdetermined nonlinear system of equations. The methods are based on a Gauss-Newton approach with line search where the search direction is found by solving a linearized problem using only a subset of the columns in the Jacobian. The choice of columns in the Jacobian is made through a greedy approach looking at either maximum descent or an approach corresponding to orthogonal matching for linear problems. The methods are shown to be convergent and efficient and outperform the $\ell_1$ approach on the test problems presented.

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Mårten Gulliksson, Anna Oleynik. 2016-10-10. Greedy Gauss-Newton algorithm for finding sparse solutions to nonlinear underdetermined systems of equations. https://arxiv.org/abs/1610.03095

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