Influence of Equality Constraints on Ill-conditioned Problems and Constrained Regularization Method

XIE Jian; ZHU Jianjun

doi:10.13203/j.whugis20130764

Volume 40 Issue 10

Oct. 2015

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Geomatics and Information Science of Wuhan University > 2015 > 40(10): 1344-1348. > DOI: 10.13203/j.whugis20130764

XIE Jian, ZHU Jianjun. Influence of Equality Constraints on Ill-conditioned Problems and Constrained Regularization Method[J]. Geomatics and Information Science of Wuhan University, 2015, 40(10): 1344-1348. DOI: 10.13203/j.whugis20130764

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Influence of Equality Constraints on Ill-conditioned Problems and Constrained Regularization Method

Department of Geosciences and Info-physics, Central South University, Changsha 410083, China

Funds: The National Natural Science Foundation of China, No. 41274010.

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Received Date: December 09, 2013
Published Date: October 04, 2015

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Abstract

Abstract

The accuracy of least square estimation can be improved and the rank deficient problem can be eliminated by using equality constraints properly. However, the influence of equality constraints in an ill-conditioned problem is not clear. Therefore, a method to transform the equality-constrained ill-posed to unconstrained problem by eliminating a part of the parameters is proposed in this paper. We firstly analyzed the influence of equality constraints on an ill-posed problem. Subsequently, the new system with equality constraints was verified by means of an example as either ill-conditioned or not depending on the original design matrix and equality constraints. We finally propose a diagnosis-regularization two-step approach to solve the equality-constrained ill-posed problem and validate its feasibility with a simulated data experiment.
- equality constraints,
- rank deficient,
- ill-condition,
- influence analysis,
- regularization

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