In recent years there has been a growing interest in the dynamics of matrix differential systems on a smooth manifold. Research effort extends to both theory and numerical methods, particularly on the manifolds of orthogonal and symplectic matrices. This paper concerns dynamical systems on the manifold OB (n) of square oblique rotation matrices, a constraint appearing in some minimization problems and in multivariate data analysis. Background and theoretical results on differential equations on OB (n) are provided. Moreover, numerical procedures preserving the structure of the solution are found among known quadratic invariant preserving methods. Numerical tests and simulations on the oblique Procrustes problem are also reported.
Geometric integration on manifold of square oblique rotation matrices
DEL BUONO, Nicoletta
;LOPEZ, Luciano
2002-01-01
Abstract
In recent years there has been a growing interest in the dynamics of matrix differential systems on a smooth manifold. Research effort extends to both theory and numerical methods, particularly on the manifolds of orthogonal and symplectic matrices. This paper concerns dynamical systems on the manifold OB (n) of square oblique rotation matrices, a constraint appearing in some minimization problems and in multivariate data analysis. Background and theoretical results on differential equations on OB (n) are provided. Moreover, numerical procedures preserving the structure of the solution are found among known quadratic invariant preserving methods. Numerical tests and simulations on the oblique Procrustes problem are also reported.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
