A parallel algorithm for computing the polar decomposition
نویسندگان
چکیده
منابع مشابه
A Parallel Algorithm for Computing the Polar Decomposition
The polar decomposition A = UH of a rectangular matrix A, where U is unitary and H is Hermitian positive semidefinite, is an important tool in various applications, including aerospace computations, factor analysis and signal processing. We consider a pth order iteration for computing U that involves p independent matrix inversions per step and which is hence very amenable to parallel computati...
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15 صفحه اولComputing 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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A new method is described for computing the singular value decomposition (SVD). It begins by computing the polar decomposition and then computes the spectral decomposition of the Hermitian polar factor. The method is particularly attractive for shared memory parallel computers with a relatively small number of processors, because the polar decomposition can be computed efficiently on such machi...
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: Parallel Computing
سال: 1994
ISSN: 0167-8191
DOI: 10.1016/0167-8191(94)90073-6