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  • 1
    Electronic Resource
    Electronic Resource
    A fully stable rational version of theQR algorithm for tridiagonal matrices (1971)
    Springer
    Numerische Mathematik 18 (1971), S. 432-441 
    Details
    ISSN: 0945-3245
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Summary A rational version of theQR algorithm for symmetric tridiagonal matrices is presented. Stability is ensured by calculating the elements of the transformed matrix by various formulas, depending on the angle of rotation. Virtual origin shifts are determined from perturbation estimates for the leading 2×2 and 3×3 submatrices; the size of these shifts can optionally serve as a convergence criterion. A number of test matrices, including one with several degeneracies, were diagonalized; an average of 1.3–1.5QR iterations per eigenvalue was needed for 12-figure precision, and of 1.7–2.0 for 22-figure precision.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01406680
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