Gradient flows computing the C-numerical range with applications in NMR spectroscopy

被引：22

作者：

Helmke, U

Hüper, K

Moore, JB

Schulte-Herbrüggen, T

机构：

[1] Univ Wurzburg, Dept Math, D-97074 Wurzburg, Germany

[2] Australian Natl Univ, Dept Syst Engn, RSISE, Canberra, ACT 0200, Australia

[3] Carlsberg Lab, Dept Chem, DK-2500 Copenhagen, Denmark

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2002年 / 23卷 / 3-4期

关键词：

C-numerical range; optimization; gradient flows; discretization; NMR spectroscopy; nilpotent matrices;

D O I：

10.1023/A:1016582714251

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：

In this paper gradient flows on unitary matrices are studied that maximize the real part of the C-numerical range of an arbitrary complex nxn-matrix A. The geometry of the C-numerical range can be quite complicated and is only partially understood. A numerical discretization scheme of the gradient flow is presented that converges to the set of critical points of the cost function. Special emphasis is taken on a situation arising in NMR spectroscopy where the matrices C,A are nilpotent and the C-numerical range is a circular disk in the complex plane around the origin.

引用

页码：283 / 308

页数：26

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