Maintianing solution invariants in the numerical solution of ODEs
SIAM Journal on Scientific and Statistical Computing
The projected gradient methods for least squares matrix approximations with spectral constraints
SIAM Journal on Numerical Analysis
Matrix computations (3rd ed.)
SIAM Journal on Scientific Computing
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
GIPSCAL revisited. A projected gradient approach
Statistics and Computing
The ℓ1 oblique procrustes problem
Statistics and Computing
First Order Error Propagation of the Procrustes Method for 3D Attitude Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Projected gradient approach to the numerical solution of the SCoTLASS
Computational Statistics & Data Analysis
Improved statistical TRE model when using a reference frame
MICCAI'07 Proceedings of the 10th international conference on Medical image computing and computer-assisted intervention - Volume Part I
On the convergence of ICA algorithms with weighted orthogonal constraint
Digital Signal Processing
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The weighted orthogonal Procrustes problem, an important class of data matching problems in multivariate data analysis, is reconsidered in this paper. It is shown that a steepest descent flow on the manifold of orthogonal matrices can naturally be formulated. This formulation has two important implications: that the weighted orthogonal Procrustes problem can be solved as an initial value problem by any available numerical integrator and that the first order and the second order optimality conditions can also be derived. The proposed approach is illustrated by numerical examples.