2013 • Other
A differential-geometric look at the Jacobi-Davidson framework
Authors:
Absil, Pierre-Antoine ,
Hochstenbach, Michiel E.
Published in:
Mathematical System Theory - Festschrift in Honor of Uwe Helmke on the Occasion of his Sixtieth Birthday
The problem of computing a p-dimensional invariant subspace of a symmetric positive-definite matrix pencil of dimension n is interpreted as computing a zero of a tangent vector field on the Grassmann manifold of p-planes in Rn. The theory of Newton’s method on manifolds is applied to this problem, and the resulting Newton equations are interpreted as block versions of the Jacobi–Davidson correction equation for the generalized eigenvalue problem.