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Locating and computing arbitrarily distributed zeros
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AI
DOI：10.1137/S1064827598333806.png)
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Abstract
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The problem of locating and computing with certainty all the simple roots of a twice continuously differentiable function f: [a, b] subset of R --> R is studied when some additional information on the distribution of the roots in the interval is available. The framework is the one proposed by [SIAM J. Sci. Comput., 17 (1996), pp. 1232-1248], where only the uniform case was examined. This paper settles some of the problems posed there and generalizes some of its results by considering an arbitrary distribution of the roots in [a, b]. The theoretical results are accompanied by simulations in a number of problems of various size.
Keywords:
zeros isolation
Kronecker-Picard theory
topological degree
locating simple roots
computing simple roots
zeros identifications
bisection method
distribution of the roots
expected complexity of algorithms
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