Numerically stable deflation of hessenberg and symmetric tridiagonal matrices |
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Authors: | P. A. Businger |
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Affiliation: | (1) Bell Telephone Laboratories, 07974 Murray Hill, New Jersey, USA |
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Abstract: | While numerically stable techniques have been available for deflating a fulln byn matrix, no satisfactory finite technique has been known which preserves Hessenberg form. We describe a new algorithm which explicitly deflates a Hessenberg matrix in floating point arithmetic by means of a sequence of plane rotations. When applied to a symmetric tridiagonal matrix, the deflated matrix is again symmetric tridiagonal. Repeated deflation can be used to find an orthogonal set of eigenvectors associated with any selection of eigenvalues of a symmetric tridiagonal matrix. |
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