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- W2039219092 abstract "To compute the eigenvalues of a skew-symmetric matrix A , we can use a one-sided Jacobi-like algorithm to enhance accuracy. This algorithm begins by a suitable Cholesky-like factorization of A , A=G T JG . In some applications, A is given implicitly in that form and its natural Cholesky-like factor G is immediately available, but “tall”, i.e., not of full row rank. This factor G is unsuitable for the Jacobi-like process. To avoid explicit computation of A , and possible loss of accuracy, the factor has to be preprocessed by a QR-like factorization. In this paper we present the symplectic QR algorithm to achieve such a factorization, together with the corresponding rounding error and perturbation bounds. These bounds fit well into the relative perturbation theory for skew-symmetric matrices given in factorized form." @default.
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- W2039219092 date "2003-01-01" @default.
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- W2039219092 title "Rounding error and perturbation bounds for the symplectic QR factorization" @default.
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- W2039219092 doi "https://doi.org/10.1016/s0024-3795(02)00263-x" @default.
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