Recursive polynomial expansion for the matrix step function uses degree-eight components evaluated in three matrix multiplications to reduce overall multiplication count versus prior recursive methods.
Schulz , Iterative berechung der reziproken matrix , ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift f \"u r Angewandte Mathematik und Mechanik, 13 (1933), pp
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A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.
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A second-order method landing on the Stiefel manifold via Newton$\unicode{x2013}$Schulz iteration
A second-order method achieves local quadratic convergence on the Stiefel manifold without retractions by combining a modified Newton tangent step with Newton-Schulz normal steps for constraint satisfaction.