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An Iterative Algorithm for Computing the Best Estimate of an Orthogonal Matrix

Björck, Å. ; Bowie, C.

SIAM journal on numerical analysis, 1971-06, Vol.8 (2), p.358-364 [Periódico revisado por pares]

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Título:
An Iterative Algorithm for Computing the Best Estimate of an Orthogonal Matrix
Autor: Björck, Å. ; Bowie, C.
Assuntos: Algorithms ; Decomposition ; Mathematical inequalities ; Mathematical theorems ; Mathematics ; Perceptron convergence procedure ; Random variables ; Sufficient conditions
É parte de: SIAM journal on numerical analysis, 1971-06, Vol.8 (2), p.358-364
Descrição: The closest unitary matrix, measured in Euclidean norm, to a given rectangular matrix A is known to be the unitary factor in the polar decomposition of A. The paper gives a family of iterative methods of order of convergence p + 1, p = 1, 2, 3, ..., for computing this matrix. The methods are especially efficient when the columns of A are not too far from being orthonormal. The choice of order of convergence to minimize the amount of computation is discussed. Global convergence properties for the methods of order ≤ 4 are studied and sufficient conditions for convergence in terms of |I - AH A| are given.
Editor: Philadelphia: Society for Industrial and Applied Mathematics
Idioma: Inglês

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