ConceptOrder-4 Polar Retraction
Fourth-Order Polar Decomposition Retraction
A numerical method that maps tangent-space updates back onto the manifold, using the matrix polar decomposition to achieve fourth-order accuracy, employed to preserve orthogonality on the Stiefel manifold.
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Nov 6
The paper optimizes on the Stiefel manifold St(k, D), using a fourth-order polar decomposition retraction together with a Neumaier compensated accumulator, and reports an orthogonality error of ||X^T X - I_k|| ≤ 10^-15 with no catastrophic drift.
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