A new MM algorithm for root‐finding problems.

The minorization–maximization (MM) algorithm is an optimization technique for iteratively calculating the maximizer of a concave target function rather than a root–finding tool. In this paper, we in the first time develop the MM algorithm as a new method for seeking the root x∗$$ {x}^{\ast } $$ of a univariate nonlinear equation g(x)=0$$ g(x)=0 $$. The key idea is to transfer the root–finding issue to iteratively calculate the maximizer of a concave target function by designing a new MM algorithm. According to the ascent property of the MM algorithm, we know that the proposed algorithm converges to the root x∗$$ {x}^{\ast } $$ and does not depend on any initial values, in contrast to Newton's method. Several statistical examples are provided to demonstrate the proposed algorithm. [ABSTRACT FROM AUTHOR]