The Geometry of Algorithms with Orthogonality Constraints

摘要: In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann Stiefel manifolds. These manifolds represent constraints that arise in such areas as symmetric eigenvalue problem, nonlinear problems, electronic structures computations, signal processing. addition to algorithms, show how geometrical framework gives penetrating insights allowing us create, understand, compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra provide top level mathematical view of previously unrelated It is our hope developers perturbation theories will benefit from theory, methods, examples paper.