Topic: Newton's method for nonlinear mappings into vector bundles
 
Abstract: We consider Newton's method for finding zeros of nonlinear mappings from amanifold X into a vector bundle E. In this setting a connection on E is requiredto render the Newton equation well defined, and a retraction on X is neededto compute a Newton update. As applications we will discuss the solution ofvariational problems involving mappings between manifolds, and, in particular,the numerical computation of geodesics under force fields.

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