Nonlinear optimization exclusion tests for finding all solutions of nonlinear equations

Exclusion tests are a well known tool in the area of interval analysis for finding the zeros of a function over a compact domain. Recently, K. Georg developed linear programming exclusion tests based on Taylor expansions. In this paper, we modify his approach by choosing another objective function and using nonlinear constraints to make the new algorithm converges faster than the algorithm in [K. Georg, A new exclusion test, J. Comput. Appl. Math. 152 (2003) 147–160]. In this way, we reduce the number of subinterval in each level. The computational complexity for the new tests are investigated. Also, numerical results and comparisons will be presented.