Bounds for integration matrices that arise in Gauss and Radau collocation

被引：18

作者：

Chen, Wanchun ^{[1
]}

Du, Wenhao ^{[1
]}

Hager, William W. ^{[2
]}

Yang, Liang ^{[1
]}

机构：

[1] Beihang Univ, Sch Astronaut, 37 Xueyuan Rd, Beijing, Peoples R China

[2] Univ Florida, Dept Math, POB 118105, Gainesville, FL 32611 USA

来源：

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS | 2019年 / 74卷 / 01期

基金：

美国国家科学基金会;

关键词：

Integration matrix; Differentiation matrix; Gauss quadrature; Radau quadrature; Collocation methods; CONVERGENCE RATE;

D O I：

10.1007/s10589-019-00099-5

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

Bounds are established for integration matrices that arise in the convergence analysis of discrete approximations to optimal control problems based on orthogonal collocation. Weighted Euclidean norm bounds are derived for both Gauss and Radau integration matrices; these weighted norm bounds yield sup-norm bounds in the error analysis.

引用

页码：259 / 273

页数：15

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