수치해석 HW1
Due: sep. 26, 10.30am
1.

a) Show that      with        sin     has a unique solution on     .

b) Use Corollary 2.5 to estimate the number of iterations required to achieve  
accuracy.
c) Perform the fixed-point iteration to find an approximation to the fixed point that
is accurate to within   with    .
2. The following four methods are proposed to compute   . Rank them in order,
based on their apparent speed of convergence, assuming   .
        

a) 


    
b)       
   
 
c)   
  


3. If  ∞
are a convergent sequence to , that is obtained by the secant

method for the root finding problem,     ,
a) then there exists
Prove the followings.
a constant    exists with
       ≈           
b)   converges to  of order     
 , that is,
  
lim   
→∞    
for some    .
4. We consider numerical roof finding methods for the equation   cos   
Perform your numerical tests,       ,
       .    .
a) Solve it by the bisection method (       )
b) Solve it by a fixed point method (    )
c) Solve it by the Newton’s method (    )
d) Solve it by the secant method (       )
e) Solve it by the method of false position. (       )
*** For each problem in (4), show the numerical results in a table as follows.

- Do not

submit your programs
    
     /      