15-05-2012, 10:53 AM
Newton Raphson Method
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Assume the function as f(x).
Find f’(x) and f’’(x).
Assume the initial value and check if its correct by checking the below condition
If the initial guess is correct proceed with the above formulae to find x2.
To check the accuracy the formulae is |x2-x1|< Accuracy.
Find x2 until and unless the accuracy check is satisfied. Or in other case till the given number of iterations are done.
Modified Newton Raphson Method.
Assume the function as f(x).
Find f’(x) and f’’(x).
Assume the initial value and check if its correct by checking the below condition
If the initial guess is correct proceed with the above formulae to find x2.
While finding the iteration 2,3,…. Use the value of f’(x) the same used in iteration 1.
To check the accuracy the formulae is |x2-x1|< Accuracy.
Find x2 until and unless the accuracy check is satisfied. Or in other case till the given number of iterations are done.
Successive Approximate or one point iteration method.
Assume the function f(x).
Find the value of x=…. from the function f(x) and assume it to be g(x).
Then find the value of g’(x).
Assume an initial guess and check it with the condition g’(x) < 1.
Then in iteration 1 find the value of g(x).
Then by assuming the initial guess as the previous answer again find g(x)
Continue it till the number of iterations to be done are fulfilled.