How i can construct Algorithm for successive values of a function

Dear All,

• Please help me to construct following algorithm
• X0(initializing vector)
• while (tol>e-4,iter<100)
• k=0,1 2...until convergent;
• compute f(Xk);% a nonlinear function
• compute Sk=f(Xk+Sk)-f(Xk);
• Xk=Xk+Sk;
• tol=gradient (f(Xk));end

Here i am facing the problem that when suppose k=0 (iteration 1),how i can get f(X0+S0)in same iteration because this is the output of second iteration.My Problem is how i can calculate the difference f(Xk+Sk)-f(Xk).In general at kth iteration i need to find

• f(Xk+Sk)-f(Sk)
• where
• f(Xk+Sk) is output that will be calcuated at (k+1)th iter
• f(Xk) is output that will be calculated at kth iter.

Answer 1

[Walter Roberson]

No, f(Xk+Sk) is not the output that will be calculated at the k+1'th iteration. It is the output of f when called upon the sum of Xk and Sk

You have the difficulty that you have not defined an initial value for Sk.

[zahid]

Sorry i did a mistake in writing this code please see now

• X0(initializing vector)
• while (tol>e-4,iter<100)
• k=0,1 2...until convergent;
• compute f(Xk);% a nonlinear function
• Compute Sk % Newton step
• compute R=f(Xk+Sk)-f(Xk);
• Sk=RSk
• Xk=Xk+Sk;
• tol=gradient (f(Xk)); end