We prove that the fixed point iteration of arbitrary positive concave mappings with nonempty fixed point set converges geometrically for any starting point. We also show that positivity is crucial for ...

Learn how to find the roots of equations using fixed-point iteration and Newton's method, two common techniques in numerical analysis. Compare their convergence, error, advantages, and disadvantages.

Abstract: We prove that the fixed point iteration of arbitrary positive concave mappings with nonempty fixed point set converges geometrically for any starting point. We also show that positivity is ...