Nonlinear Equations in One Variable
One of the most important tasks in scientific computing is the problem of finding zeros (or roots) of nonlinear functions. In classical numerical analysis, root-finding methods for nonlinear functions begin with an approximation and apply an iterative method (such as Newton’s or Halley’s methods), which hopefully improves the approximation. It is a myth that no numerical algorithm is able to compute all zeros of a nonlinear equation with guaranteed error bounds, or even more, that no method is able to give concrete information about the existence and uniqueness of solutions of such a problem.
KeywordsInterval Arithmetic Extended Interval Error Code Actual Interval Interval Vector
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