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VOL. 22 | 1993 Lax Equations Associated with a Least Squares Problem and Compact Lie Algebras

Abstract

The gradient flow in a least squares problem on a Lie group takes a Lax form [8]. We associate the Lax equation with homogeneous spaces and symmetric spaces of compact simple Lie groups. The critical points of the Lax equation lie in the Cartan subalgebras of the simple Lie algebras. A reduction from homogeneous spaces to symmetric spaces is described by a ‘coalescence’ of roots. For the complex Grassmann manifold, it is shown that an initial value problem of the Lax equation can be uniquely solved. Some applications to a least squares fitting problem and a linear programming problem are discussed.

Information

Published: 1 January 1993
First available in Project Euclid: 15 August 2018

zbMATH: 0799.58031
MathSciNet: MR1274950

Digital Object Identifier: 10.2969/aspm/02210213

Rights: Copyright © 1993 Mathematical Society of Japan

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Vol. 22 • 1 January 1993
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