On computational efficiency for multi-precision zero-finding methods

An adapted definition related to multi-precision arithmetic zero-finding methods is considered and several improvements to iterative methods to compute nonlinear equation solutions, which increase the local order of convergence are revisited. Furthermore, a higher efficiency when we use a definition related to adaptive multi-precision arithmetic is also given. Numerical results computed with a floating point system representing 200 and 1000 decimal digits support this theory.