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    Convergence of Newton's method for a single real equation (1985)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TP-2489 , NAS 1.60:2489
    Format: application/pdf
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