Computing the Polar Decomposition—with Applications
نویسندگان
چکیده
منابع مشابه
Computing the Polar Decomposition—with Applications
A quadratically convergent Newton method for computing the polar decomposition of a full-rank matrix is presented and analysed. Acceleration parameters are introduced so as to enhance the initial rate of convergence and it is shown how reliable estimates of the optimal parameters may be computed in practice. To add to the known best approximation property of the unitary polar factor, the Hermit...
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15 صفحه اولComputing 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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In this paper we propose a new approach to plane partitioning with similar features to those of Polar Diagram, but we assume that the pole is close to the sites. The result is a new tessellation of the plane in regions called Near Pole Polar Diagram NPPD. Here we define the (NPPD) of points, the dual and the Contracted dual of it, present an optimal algorithms to draw them and discuss the appli...
متن کاملBackward Stability of Iterations for Computing the Polar Decomposition
Among the many iterations available for computing the polar decomposition the most practically useful are the scaled Newton iteration and the recently proposed dynamically weighted Halley iteration. Effective ways to scale these and other iterations are known, but their numerical stability is much less well understood. In this work we show that a general iteration Xk+1 = f(Xk) for computing the...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific and Statistical Computing
سال: 1986
ISSN: 0196-5204,2168-3417
DOI: 10.1137/0907079