Exam (elaborations)
COS2633 EXAM PACK 2023
- Course
- COS2633 (COS2633)
- Institution
- University Of South Africa (Unisa)
QUESTIONS AND ANSWERS
[Show more]
Content preview
COS2633EXAM
PACK 2023
QUESTIONS WITH ANSWERS
,COS2633
EXAM
PACK 2023
LATEST
QUESTIONS
AND ANSWERS
For queries or any assignment help
Email: musyokah11@gmail.com
,COS2633
EXAM PACK
Revision PACK
Questions. Answers
, NUMERICAL METHODS I – COS 233-8
Interval bisection method
Strategy Find two values of x, that is, a and b, which bracket the root by checking whether f ( a ) × f (b) < 0. Then
successively divide the interval in half and replace one endpoint with the midpoint so that the root is
bracketed again.
Requirements The function f(x) must be continuous in the interval.
There should not be multiple roots in the interval.
Advantages The number of iterations to achieve a specified accuracy is known in advance.
It is the method that is recommended for finding a first approximation to the root.
Convergence Slow because the estimate of the root may be better at an earlier iteration than at later ones.
Order of convergence 1
(b − a )
Error formula e=
2n
Note This does not mean that each error is smaller than the previous one.
Secant method
Strategy Choose two values of x, that is, x 0 and x1 , which are close to the root. Draw a straight line through the
points (these points can either be on the same side or on opposites sides of the root). The intersection of
the line with the x-axis should be close to the root. Repeat the process by always using the last two
computed values.
Requirements The function f(x) must be continuous.
The function f(x) must not be far from linear in the vicinity of the root.
Convergence Intermediate because the error is proportional to the product of the previous two errors. It is therefor
faster than a linear method but slower than a quadratic method.
Order of convergence 1.62
f ( xn )
Iteration formula x n +1 = x n − ( x n − x n −1 )
f ( x n ) − f ( x n −1 )
g ′′( ξ1 , ξ2 )
Error formula en +1 = (e n )(en −1 )
2
1+ 5
Note The order of convergence is = 1.62 .
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller mpumeleloh. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R50,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
82871 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now