What is fixed point in fixed-point iteration method Fixed point A point, say, s is called a fixed point if it satisfies the equation x g(x) . Fixed point Iteration The transcendental equation f(x) 0 can be converted algebraically into the form x g(x) and then using the iterative scheme with the recursive relation. 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 this result to hold, and the concept of (nonlinear) spectral radius of asymptotic mappings provides us with information about the convergence factor. As a. Jim Lambers MAT 460560 Fall Semester 2009-10 Lecture 9 Notes These notes correspond to Section 2.2 in the text. Fixed-point Iteration A nonlinear equation of the form f(x) 0 can be rewritten to obtain an equation of the form g.