A minimal norm corrected underdetermined Gauß-Newton procedure

Authors:
Stephen L. Campbell;Peter Kunkel;Karen Bobinyec
Affiliations:
Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, USA;Mathematisches Institut, Universität Leipzig, Johannisgasse 26, 04009 Leipzig, Federal Republic of Germany;Department of Mathematics, Box 8205, North Carolina State University, Raleigh, NC 27695-8205, USA
Venue:
Applied Numerical Mathematics
Year:
2012

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Abstract

If a Gausz-Newton iteration is used to solve a system of equations that has a manifold of solutions, then the iteration does not produce the minimal norm solution. The limit of the iteration depends on the starting point. This paper introduces a modified Gausz-Newton method that is designed to keep the nonunique part of the solution small in some sense. The iteration is analyzed. Its behavior is discussed along with two computational examples that include the iteration@?s application to general integration methods for differential algebraic equations.