Newton's method on Riemannian manifolds and a geometric model for the human spine

To study a geometric model of the human spine we are led to finding a constrained minimum of a real valued function defined on a product of special orthogonal groups. To take advantge of its Lie group structure we consider Newton's method on this manifold. Comparisons between measured spines an...

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Veröffentlicht in:	IMA journal of numerical analysis 2002-07, Vol.22 (3), p.359-390
Hauptverfasser:	Adler, Roy L., Dedieu, Jean‐Pierre, Margulies, Joseph Y., Martens, Marco, Shub, Mike
Format:	Artikel
Sprache:	eng
Schlagworte:	Calculus of variations and optimal control Exact sciences and technology Global analysis, analysis on manifolds human spine Mathematical analysis Mathematics Newton's method Nonlinear algebraic and transcendental equations Numerical analysis Numerical analysis. Scientific computation orthogonal group Riemannian manifold Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
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Beschreibung
Zusammenfassung:	To study a geometric model of the human spine we are led to finding a constrained minimum of a real valued function defined on a product of special orthogonal groups. To take advantge of its Lie group structure we consider Newton's method on this manifold. Comparisons between measured spines and computed spines show the pertinence of this approach.
ISSN:	0272-4979 1464-3642
DOI:	10.1093/imanum/22.3.359