## Abstract and Applied Analysis

### The Derivation of Structural Properties of LM-g Splines by Necessary Condition of Optimal Control

#### Abstract

The structural properties of LM-g splines are investigated by optimization and optimal control theory. The continuity and structure of LM-g splines are derived by using a class of necessary conditions with state constraints of optimal control and the relationship between LM-g interpolating splines and the corresponding L-g interpolating splines. This work provides a new method for further exploration of LM-g interpolating splines and its applications in the optimal control.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 641435, 5 pages.

Dates
First available in Project Euclid: 6 October 2014

https://projecteuclid.org/euclid.aaa/1412606208

Digital Object Identifier
doi:10.1155/2014/641435

Mathematical Reviews number (MathSciNet)
MR3206808

Zentralblatt MATH identifier
07022805

#### Citation

Liu, Xiongwei; Zhang, Xinjian; Cheng, Lizhi. The Derivation of Structural Properties of LM-g Splines by Necessary Condition of Optimal Control. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 641435, 5 pages. doi:10.1155/2014/641435. https://projecteuclid.org/euclid.aaa/1412606208

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