Geometric Integration on Manifold of Square Oblique Rotation Matrices
Nicoletta Del Buono, Luciano Lopez · SIAM Journal on Matrix Analysis and Applications · 2002
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 ${\cal OB}(n)$ 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 ${\cal OB}(n)$ 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.