Efficient Numerical Methods for Solving Equations: MCQs and Solutions

[abrowaqas]

some one help me to solve these questions.

1. The order of convergence of Newton-Raphson Method is
a) at least one b) at most two c) at least there d) four e) none of these.

2. Newton-Raphson Method fails to find the root of f(x)=0 if:
a) f'(x) > 0 b) f(x)< 0 c) f'(x) = 0 d) f'(x) <0 e) non of these.

3. the fixes point iteration method defined in the form Xn+1 = g(Xn) converges of:
a) g'(x)>1 b) g'(x) =1 c) g'(x)>1 d) g'(x)=0 e) None of these

4. Jacobi Method for system of linear equations has convergence:
a) faster than SOR method b) faster than Gauss_siedel c) faster than Newton's method d)slower than Gauss-siedel e) none of these

 

[HallsofIvy]

I presume you have read the rules for this forum- which you were supposed to have read before you registered. If so, you know that you must show what you have tried before asking for help. I don't see that here.

 

[abrowaqas]

well ... the questions are typically related to theory of the topics.
so the guess may works. .
for
1. i don't have idea

2. i think its f'(x)=0 bcoz if the derivative is zero Newtons-raphson will not approach to infinity

3. none of these coz for iteration to converge it must have decreasing derivatives

4. faster than gauss-seidel...

am i right ... kindly suggest