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The geometry of algorithms with orthogonality constraints. (English) Zbl 0928.65050

The paper offers a new approach to the algorithms in numerical analysis involving orthogonality constraints. As a concluding example of the insight gained, a Grassmann based taxonomy for problems related to the symmetric eigenproblem is proposed. Some Newton and conjugate gradient methods are developed on the Grassmann and Stiefel manifolds that arise in such areas as symmetric or nonlinear eigenvalue problem. The theory proposed provides a taxonomy for numerical linear algebra algorithms that gives a top level mathematical view of many algorithms.

MSC:

65F15 Numerical computation of eigenvalues and eigenvectors of matrices
81V55 Molecular physics

Software:

JDQZ
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