A minimal norm corrected underdetermined Gauss-Newton procedure

作者：Campbell Stephen L^*; Kunkel Peter; Bobinyec Karen

来源：Applied Numerical Mathematics, 2012, 62(5): 592-605.

DOI：10.1016/j.apnum.2012.01.006

• Nonlinear equations
• Least squares solutions
• Minimal norm solutions
• Modified Gauss-Newton method
• Differential algebraic equations

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 iteration%26apos;s application to general integration methods for differential algebraic equations.

• 出版日期2012-5