algorithm程序讲解、辅导Matlab语言编程、Matlab程序讲解

Computer Assignment 2
Thurs 10/16, 11pm
(a) Develop a Matlab code to implement the fixed point algorithm.
Algorithm: (Exactly as given in the textbook)
START PROGRAM
INPUT/INITIALIZATION : Input approximation po; Tolerance T OL;
maximum number of iterations No.
OUTPUT : Approximate Solution p or message of failure.
STEP 1 Set i = 1.
STEP 2 While i ≤ No repeat Steps 3 - 6 :
STEP 3 Set p = g(po). Compute pi
STEP 4 If | p − po |< T OL then
OUTPUT (p) the procedure was successful
STOP
STEP 5 Set i = i + 1.
STEP 6 Set po = p. Update po
STEP 7 OUTPUT (’ The method failed after No iterations, No =’, No);
The procedure was unsuccessful.
END PROGRAM
You may use a ”for” loop or a ”while” loop to implement the iteration. Also
output your error in the form a graph to easily visualize the iteration and convergence.
(b) Develop a Matlab code to implement Newton’s method.
Algorithm: (Exactly as given in the textbook)
START PROGRAM
INPUT/INITIALIZATION : Input approximation po; Tolerance T OL;
maximum number of iterations No.
OUTPUT : Approximate Solution p or message of failure.
1
STEP 1 Set i = 1.
STEP 2 While i ≤ No repeat Steps 3 - 6 :
STEP 3 Set p = po − f(po)/f0
(po). Compute pi
STEP 4 If | p − po |< T OL then
OUTPUT (p) the procedure was successful
STOP
STEP 5 Set i = i + 1.
STEP 6 Set po = p. Update po
STEP 7 OUTPUT (’ The method failed after No iterations, No =’, No);
The procedure was unsuccessful.
END PROGRAM
(c) Use the iteration method, and Newton’s method to find the fixed point of
g(x) = x/2 + 1/x in [1, 2] to approximate √
2 accurately to within 10−5
. Which
method converges faster?
(d) Use your algorithms to solve problem 18 in Sec. 2.2.
Some new commands :
Example 1 :
Commands for printing in Matlab.
output = sprintf(’Any text you want’);
disp(output);
This will print the string of characters ‘Any text you want’ on the command
window.
Example 2 :
To print character strings with number :
p = 1.45637798423;
output = sprintf(’Any text you want %f’,p);
disp(output);
When you use %f you instruct matlab to replace with the number in p showing
only 6 digits past the decimal point with a round off.
This will print on the command window :
Any text you want 1.456378
Example 3 :
p = 1.45637798423;
output = sprintf(’Any text you want %0.10f’,p);
disp(output);
2
This will print on the command window :
Any text you want 1.45637798423;
When you use %0.10f you instruct matlab to replace with the number in p
showing the first 10 significant digits.
Example 3 :
p = 0.000012345;
output = sprintf(’Any text you want %e’,p);
disp(output);
This will print on the command window :
Any text you want 1.234500e-5;
3