@article{campbell_kunkel_bobinyec_2012, title={A minimal norm corrected underdetermined Gauss-Newton procedure}, volume={62}, DOI={10.1016/j.apnum.2012.01.006}, abstractNote={If a Gauß–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 Gauß–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 iterationʼs application to general integration methods for differential algebraic equations.}, number={5}, journal={Applied Numerical Mathematics}, author={Campbell, Stephen and Kunkel, P. and Bobinyec, K.}, year={2012}, pages={592–605} }
@inproceedings{bobinyec_campbell_kunkel_2012, title={Constructing observers for linear time varying DAEs}, DOI={10.1109/cdc.2012.6426989}, abstractNote={This paper presents an approach for the construction of both full order and reduced order observers for general linear time varying differential algebraic equations. The necessary theory is presented. Computational issues are elaborated on, and a six dimensional example of an index two electrical circuit is solved as an illustration.}, booktitle={2012 IEEE 51st IEEE Conference on Decision and Control (CDC)}, publisher={IEEE}, author={Bobinyec, Karen and Campbell, Stephen L. and Kunkel, Peter}, year={2012}, pages={5749–5754} }