A minimal norm corrected underdetermined Gauß–Newton procedure

doi:10.1016/j.apnum.2012.01.006

Applied Numerical Mathematics

Volume 62, Issue 5, May 2012, Pages 592-605

https://doi.org/10.1016/j.apnum.2012.01.006 Get rights and content

Abstract

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.

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Cited by (0)

¹: Research supported in part by NSF Grant DMS-0907832.

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A minimal norm corrected underdetermined Gauß–Newton procedure

Abstract

Math. Comput. Modelling

J. Math. Anal. Appl.

Linear Algebra Appl.

J. Comput. Appl. Math.

Appl. Numer. Math.

J. Comput. Appl. Math.

Linear Algebra Appl.

Nonlinear Anal. Theory Methods Appl.

Constrained least squares methods for linear time varying DAE systems

Numer. Math.

Comparing stability properties of three methods in DAEs or ODEs with invariants

BIT

Analytical and numerical solutions to higher index linear variable coefficient DAE systems

J. Comput. Appl. Math.

On iterative methods for solving nonlinear least squares problems over convex sets

Israel J. Math.

Numerical Solution of Initial-Value Problems in Differential–Algebraic Equations