If a root of f(x) = 0 lies in the interval [a, b], then find the minimum number of iterations required when the permissible error is E.
If a root of f(x) = 0 lies in the interval [a, b], then find the minimum number of iterations required when the permissible error is E.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
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If a root of f(x) = 0 lies in the interval [a, b], then find the minimum number of iterations required when the permissible error is E.
![11.
Hint:
If a root of f(x) = 0 lies in the interval [a, b], then find the minimum number of iterations required
when the permissible error is E.
Answer Key:
11. n ≥
loge
:.
loge
- a
E
2
Example 3. Determine the minimum number of iterations required to solve
f(x) = x³ + 4x² − 10 = 0 by using Bisection method over [1, 2] with an accuracy 10-³.
Sol. Let n be number of iterations required to solve f (x) = 0 over [1, 2] = [a, b], then
logº |b − a |− logę €, where ε = 10-³
log 2
-
n>
log 1-log, 10-³
loge 2
The minimum number of iterations 10.
n>
=
=
3 loge
10%e
10
2
= 9.96 = 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbc49668-6c24-4a22-8f61-417f47b3692e%2Fd8817667-a2d4-4a2c-829e-40b744e054d5%2Fjzlys7p_processed.png&w=3840&q=75)
Transcribed Image Text:11.
Hint:
If a root of f(x) = 0 lies in the interval [a, b], then find the minimum number of iterations required
when the permissible error is E.
Answer Key:
11. n ≥
loge
:.
loge
- a
E
2
Example 3. Determine the minimum number of iterations required to solve
f(x) = x³ + 4x² − 10 = 0 by using Bisection method over [1, 2] with an accuracy 10-³.
Sol. Let n be number of iterations required to solve f (x) = 0 over [1, 2] = [a, b], then
logº |b − a |− logę €, where ε = 10-³
log 2
-
n>
log 1-log, 10-³
loge 2
The minimum number of iterations 10.
n>
=
=
3 loge
10%e
10
2
= 9.96 = 10
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