Abstract
This paper is concerned with iterative procedures for finding real roots of rational polynomials, and in particular with notions of efficiency for such procedures. For a measure of efficiency, similar to Ostrowski’s index but based on the number of elementary arithmetic operations used, the main theorem provides an upper bound. This bound is attained for quadratic polynomials by Newton’s method. Some open problems and conjectures of a theoretical nature are presented.
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© 1972 Plenum Press, New York
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Paterson, M.S. (1972). Efficient Iterations for Algebraic Numbers. In: Miller, R.E., Thatcher, J.W., Bohlinger, J.D. (eds) Complexity of Computer Computations. The IBM Research Symposia Series. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2001-2_5
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DOI: https://doi.org/10.1007/978-1-4684-2001-2_5
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4684-2003-6
Online ISBN: 978-1-4684-2001-2
eBook Packages: Springer Book Archive