Newton interpolary difference formula

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SUMMARY

The discussion centers on the Newton interpolary difference formula, specifically addressing the calculation of the second divided difference using the formula f(x1, x2) - f(x0, x1) / (x2 - x0). The user attempted to compute this difference with specific values, resulting in a final answer of -0.143. The values used in the calculation were f(x1, x2) = 0.510 * 0.381 and f(x0, x1) = 0.521 * 0.510, with x2 = 2.6 and x0 = 2.1.

PREREQUISITES
  • Understanding of Newton's interpolation method
  • Familiarity with divided differences
  • Basic algebraic manipulation skills
  • Knowledge of function evaluation at specific points
NEXT STEPS
  • Study the derivation of the Newton interpolary difference formula
  • Learn how to compute higher-order divided differences
  • Explore applications of Newton's interpolation in numerical analysis
  • Practice with different sets of data points to reinforce understanding
USEFUL FOR

Students studying numerical methods, mathematicians interested in interpolation techniques, and educators teaching calculus or numerical analysis concepts.

fonseh
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Homework Statement


I don't understand the meaning of the formula... For the circled part in the first photo , what is the meaning of f(x1 ,x2 ) ? and also f(x0 , x1 ) ?

Homework Equations

The Attempt at a Solution


I used the highlighted formula to find the second divided difference . But , Here's what i gt :

f(x1 ,x2 ) - f(x0 , x1 ) / ( x2 -x0 )
=
(0.510*0.381)-(0.521*0.510) / (2.6-2.1) , I ended up getting -0.143
 

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fonseh said:

Homework Statement


I don't understand the meaning of the formula... For the circled part in the first photo , what is the meaning of f(x1 ,x2 ) ? and also f(x0 , x1 ) ?

Homework Equations

The Attempt at a Solution


I used the highlighted formula to find the second divided difference . But , Here's what i gt :
(0.510*0.381)-(0.521*0.510) / (2.6-2.1) , I ended up getting -0.143

Do not post images; type out your work.
 
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Likes   Reactions: fonseh
Ray Vickson said:
Do not post images; type out your work.
It's just the notes ... For my trial , i didnt post images ...
 

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