Access over 20 million homework & study documents

Ch 3 3 interpolation newton gregory

Content type
User Generated
Rating
Showing Page:
1/13

Sign up to view the full document!

lock_open Sign Up
Showing Page:
2/13

Sign up to view the full document!

lock_open Sign Up
Showing Page:
3/13

Sign up to view the full document!

lock_open Sign Up
End of Preview - Want to read all 13 pages?
Access Now
Unformatted Attachment Preview
Numerical Analysis Interpolation Chap 3_3 1 Equally Spaced Data (Newton Gregory Interpolation) 2 Newton Gregory Interpolation β€’ If the x values are evenly spaced, the interpolating polynomial of degree n can be written in terms of the ordinary differences with x evaluate at S 𝑛 𝑃𝑛 𝑆 = ෍ π‘˜=0 𝑆 π‘˜ βˆ† 𝑓0 π‘˜ π‘₯ βˆ’ π‘₯0 𝑆= β„Ž 𝑆 𝑠 βˆ’ 1 𝑠 βˆ’ 2 … (𝑆 βˆ’ π‘˜ + 1) 𝑆 = π‘˜ π‘˜! βˆ†π‘› 𝑓𝑖 = βˆ†π‘›βˆ’1 𝑓𝑖+1 βˆ’ βˆ†π‘›βˆ’1 𝑓𝑖 3 Recall the Newton forward difference polynomial 4 Example β€’ compute the interpolating polynomial p3(x) that fits the data equally spaced, with spacing h = 1. 5 Solution β€’ equally spacing h = 1 β€’ s = (x - x0)/h = x + 1 6 βˆ†π‘› 𝑓𝑖 = βˆ†π‘›βˆ’1 𝑓𝑖+1 βˆ’ βˆ†π‘›βˆ’1 𝑓𝑖 i 0 x -1 𝑓𝑖 3 βˆ†1 𝑓𝑖 βˆ†2 𝑓𝑖 βˆ†3 𝑓𝑖 -4-3=-7 1 0 -4 9 - - 7 =16 5- - 4=9 2 1 5 -20-16=-36 -11-9= -20 -6 – 5=-11 3 2 -6 7 8 Example 3 β€’ Consider the following data, find f(1.83) i 0 1 2 3 4 x 1 3 5 7 9 𝑓𝑖 0 1.0986 1.6094 1.9459 2.1972 9 Example 3 Solution i 0 x 1 𝑓𝑖 0 βˆ†π‘› 𝑓𝑖 = βˆ†π‘›βˆ’1 𝑓𝑖+1 βˆ’ βˆ†π‘›βˆ’1 𝑓𝑖 βˆ†1 𝑓𝑖 βˆ†2 𝑓𝑖 βˆ†3 𝑓𝑖 βˆ†4 𝑓𝑖 1.0986 1 3 1.0986 -0.5878 0.5108 2 5 1.6094 0.4135 -0.1747 0.3365 3 7 1.9459 -0.3244 0.0891 -0.0852 0.2513 4 9 2.1972 10 Example 3 Solution…cont 11 Exercise 2 Estimate f (3.17)from the data using Newt ...
Purchase document to see full attachment
User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

Anonymous
Just what I was looking for! Super helpful.

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4