High-Order Retractions on Matrix Manifolds Using Projected Polynomials
نویسندگان
چکیده
منابع مشابه
High-order Retractions on Matrix Manifolds Using Projected Polynomials
We derive a family of high-order, structure-preserving approximations of the Riemannian exponential map on several matrix manifolds, including the group of unitary matrices, the Grassmannian manifold, and the Stiefel manifold. Our derivation is inspired by the observation that if Ω is a skew-Hermitian matrix and t is a sufficiently small scalar, then there exists a polynomial of degree n in tΩ ...
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This paper deals with constructing retractions, a key step when applying optimization algorithms on matrix manifolds. For submanifolds of Euclidean spaces, we show that the operation consisting of taking a tangent step in the embedding Euclidean space followed by a projection onto the submanifold, is a retraction. We also show that the operation remains a retraction if the projection is general...
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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2018
ISSN: 0895-4798,1095-7162
DOI: 10.1137/17m1130459