Algorithms for the Weighted Orthogonal Procrustes Problem and other Least Squares Problems

  title={Algorithms for the Weighted Orthogonal Procrustes Problem and other Least Squares Problems},
  author={Thomas Viklands},
  • Thomas Viklands
  • Published 2005
In this thesis, we present algorithms for local and global minimization of some Procrustes type problems. Typically, these problems are about rotating and scaling a known set of data to fit another set with applications related to determination of rigid body movements, factor analysis and multidimensional scaling. The known sets of data are usually represented as matrices, and the rotation to be determined is commonly a matrix Q with orthonormal columns. The algorithms presented use Newton and… CONTINUE READING
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Publications referenced by this paper.
Showing 1-10 of 15 references

The Geometry of Algorithms with Orthogonality Constraints

SIAM J. Matrix Analysis Applications • 1998
View 4 Excerpts
Highly Influenced

Least Squares with a Quadratic Constraint

W. Gander
Numer. Math., 36:291–307 • 1981
View 3 Excerpts
Highly Influenced

On minimization on Stiefel manifolds

European Journal of Operational Research • 2002
View 2 Excerpts

A Procrustes problem on the Stiefel manifold

Numerische Mathematik • 1999
View 3 Excerpts

A solution to the weighted procrustes problem in which the transformation is in agreement with the loss function

J. C. Lingoes
Psychometrika • 1995

On Condition Numbers and Algorithms for Determining a Rigid Body Movement

I. Söderkvist, Per-Åke Wedin
BIT, 34:424–436, • 1994
View 2 Excerpts

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