Extended interval Newton method based on the precise quotient set (Q644874)

The author considers the extended interval Newton method. Adopting a recent definition of the extended interval division by Kulisch et al., some fundamental properties of the extended interval Newton method based on the so-called precise quotient set are proved. On this basis, an algorithm and a convenient program package are developed. The performance of the algorithm is demonstrated by several practical examples and shows that it can compute correct enclosures of all zeros of the functions with high efficiency, particularly in cases where other methods are less effective.