Newton's method for concave operators with resolvent positive derivatives in ordered Banach spaces
The authors prove a non-local convergence result for Newton's method applied to a class of concave operator equations with resolvent positive derivatives in ordered Banach spaces. The key tools in their approach are special notions of concavity and the spectral theory of resolvent positive operators. Finally, the results are illustrated by applications to a number of rational matrix equations arising in various control and realization problems.
scientific article; zbMATH DE number 1903557
scientific article