how to determine the value for εs if it is not given in the question?

for newton raphson

[Amish]

Can you add more details about the question?

Answer 1

[John D'Errico]

Talk to your teacher, i.e., the person who gave you the assignment. As it is, we cannot possibly know what the unknown parameter means to you, even though you have indicated the question is about Newton-Raphson. We cannot read your mind.

And, yes, your question really has nothing to do with MATLAB. Really, your question is specifically about an assignment that was given to you. The only person who can answer that is the one who gave you the assignment.

Ok, MAYBE, I might take a wild guess, a completely random swipe at the issue, and guess that epsilon in your question is some sort of convergence tolerance. As such, that is entirely your choice to make. Only you know how important it is to you, to tighten the estimate of your solution. Even there of course, you would need to recognize that a convergence tolerance is not always the right thing to focus on. For example...

Suppose I asked you to solve the probl;em

0.333333*x - 1 == 0

And, yes, I know this is about the most utterly trivial problem to solve, MAYBE. But is it?

That is, is this really a question to solve the problem

1/3*x - 1 == 0

if so, then the answer is x==3, exactly. But if the problem is posed as it is, then we might argue the solution is

format long
x = 1/0.333333

x = 
   3.000003000003000

HOWEVER, even there, I have a problem, in that we should not be computing an exact solution to an approximate problem, and believing the result is now exact. I think too many people make this mistake.

As such, it should be argued that we should not be looking for a convergence tolerance that is tighter than the precision inherant in the constants in our problem.

Or, maybe all of this is just wild speculation. Just talk to your teacher.