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
/
0
