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関西可積分系セミナー (2002年3月12日)

日時
2002年3月12日(火)15時-16時30分
場所
京都大学本部キャンパス工学部総合校舎406会議室
吉澤真太郎 (Wuerzburg Univ., Germany)
Component Extraction Flows and Double Bracket Flows

We discuss a novel perspective between extraction of invariant subspace for a symmetric positive definite matrix and Hamiltonian systems. The motivation occures from triple directions.

The first is the geometry of Hamiltonian flows on homogeneous spaces disccussed by Thimm(1981), Bloch-Brockett-Crouch(1997), Bloch-Krishnaprasad-Marsden-Ratiu(1996).

The second comes from the information processing systems, in where Neural Network scientist are discussing the principal and minor component analysis, and also independent component analysis.

The third is NON-convex duality theory discussed by Ekeland (1977).

In this talk, I try to explain that the Legendre duality plays an important role between non-constrained optimization and constrained optimization in view of nonlinear dynamical systems including double bracket systems with “deformation” parameters. From this trick we can see a kind of the phase space compactification for the dynamical systems.