Modified secant method

A full rank update version of the secant method (t-secant) is given in single variable case.

An efficient linearization method for solving a system of nonlinear equations was developed, showing good stability and convergence properties. It uses an unconventional and simple strategy to improve the performance of classic methods by a full-rank update of the Jacobian approximates. It can be considered both as a discretized Newton’s method or as a quasi-Newton method with a full-rank update of the Jacobian approximates. Numerical examples are shown for demonstration purposes.