Bisection Method: Please explain Step 6 for me in DETAILS, here is the algorithm
ID: 2963984 • Letter: B
Question
Bisection Method:
Please explain Step 6 for me in DETAILS, here is the algorithm:
Step 1 Set i = 1
FA = f(a)
Step 2 While i<=No do Steps 3-6
Step 3 Set p = a + (b - a )/2; ( Compute pi.)
FP = f(p).
Step 4 If FP = 0 or (b-a)/2 < TOL then
OUTPUT (p); (Procedure completed successfully.)
STOP.
Step 5 Set i = i + 1.
Step 6 if FA*FP > 0 then set a = p; (Compute ai, bi.)
FA = FP
else set b = p. (FA is unchanged.)
Step 7 OUTPUT ('Method failed after No iterations, No =', No);
(The procedure was unsuccessful.)
STOP.
PLEASE EXPLAIN STEP 6 FOR ME IN DETAILS FOR NEWTON'S METHOD:
Newton's Method:
INPUT initial approximation p0; tolerance TOL; maximum number of iterations No.
OUTPUT approximate solution p or message of failure.
Step 1 Set i = 1.
Step 2 While i<= No do Steps 3-6.
Step 3 Set p = po - f(po)/f '(po). (Compute pi.)
Step 4 If |p - po | < TOL 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 iteration, No =', No);
(The procedure was unsuccessful.)
STOP.
Explanation / Answer
bisection method
Step 6 if FA*FP > 0 then set a = p; (Compute ai, bi.)
FA = FP
else set b = p. (FA is unchanged.)
explanation:-
if FA*FP>0 that means that FA as well as FP are positive so in step 3 a is replaced by value of p esle b is replaced by p.
Newton's Method:
Step 6 Set po = p. (Update po.)
explanation
replace po by p in step 3 and compute the further iterations
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