Symbolic-numeric nonlinear equation solving

Authors:
Kelly Roach
Affiliations:
Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Venue:
ISSAC '94 Proceedings of the international symposium on Symbolic and algebraic computation
Year:
1994

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Abstract

A numerical equation-solving algorithm employing differentiation and interval arithmetic is presented which finds all solutions of f(z) = 0 on an interval I when f is holomorphic and has simple zeros. A two dimensional generalization of this algorithm is discussed. Finally, aspects of a broader symbolic-numeric algorithm which uses the first algorithm as a foundation are considered.