Search results with tag "Point iteration"
Rate of Convergence - Gordon College
www.math-cs.gordon.eduFixed-Point Iterations Many root- nding methods are xed-point iterations. These iterations have this name because the desired root ris a xed-point of a function g(x), i.e., g(r) !r. To be useful for nding roots, a xed-point iteration should have the property that, for xin some neighborhood of r, g(x) is closer to rthan xis. This leads to the ...
2.2 Fixed-Point Iteration - University of Notre Dame
www3.nd.edu• A number is a fixed point for a given function if = • Root finding =0 is related to fixed-point iteration = –Given a root-finding problem =0, there are many with fixed points at : Example: ≔ − ≔ +3 … If has fixed point at , then = − ( ) has
The Shooting Method for Two-Point Boundary Value …
www.math.usm.edumethod, xed-point iteration, Newton’s Method, or the Secant Method. The only di erence is that each evaluation of the function y(b;t), at a new value of t, is relatively expensive, since it requires the solution of an IVP over the interval [a;b], for which y0(a) = t. The value of that solution at
Chapter 1 Iteration - MathWorks
www.mathworks.comis the simplest while loop for our fixed point iteration. x = 3 while x ~= sqrt(1+x) x = sqrt(1+x) end This produces the same 32 lines of output as the for loop. However, this code is open to criticism for two reasons. The first possible criticism involves the termi-nation condition. The expression x ~= sqrt(1+x) is the Matlab way of writing