The Fréchet Derivative of the Polar Decomposition
نویسندگان
چکیده
We derive iterative methods for computing the Fréchet derivative of the map which 6 sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has 7 orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices 8 as well as rectangular matrices having more rows than columns. Our derivation relies on a novel 9 identity that relates the Fréchet derivative of the polar decomposition to the matrix sign function 10 sign(X) = X(X2)−1/2 applied to a certain block matrix X. 11
منابع مشابه
Iterative Computation of the Fréchet Derivative of the Polar Decomposition
We derive iterative methods for computing the Fréchet derivative of the map which sends a full-rank matrix A to the factor U in its polar decomposition A = UH, where U has orthonormal columns and H is Hermitian positive definite. The methods apply to square matrices as well as rectangular matrices having more rows than columns. Our derivation relies on a novel identity that relates the Fréchet ...
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