Improving Newton's Method for the Mollweide Projection Equation

This article explores using Newton's method to solve a crucial equation in the Mollweide map projection. Near high latitudes (approaching π/2), the equation presents a double root, causing Newton's method to slow down or diverge. The article proposes a modified Newton's method, adjusting parameter 'm' to improve convergence speed and accuracy near the double root. However, challenges remain very close to the double root, leading the author to suggest combining it with other methods like power series inversion for a complete solution.