Gauss Forward And Backward Central Difference Interpolation Formula

This PPT contains the topic called Gauss Forward And Backward Central Difference Interpolation Formula of subject called Numerical and Statistical Methods for Computer Engineering.

1. Presentation on Gauss Forward And Backward Central Difference Interpolation Formula Presented By : Deep Dalsania (160350116002) Jhanvi Ghediya (160350116003) Rakesh Talaviya (160350116010) Drashti Bangoriya (160350116001) Bhakti Tank (160350116011) Subject Name: Numerical and Statistical Methods For Computer Engineering Subject Code: 2140706 Submitted To: Prof. Dipesh Bhogayata Sir

2. INTERPOLATION The process of finding the curve passing through the points is called as Interpolation. INTERPOLATION EQUAL INTERVAL UNEQUAL INTERVAL NEWTOWN AND GAUSS INTERPOLATION LAGRANGES INTERPOLATION

3. Gauss Forward Central Difference Formula Y= f(x) = P n (x) = Y + PΔY + P (P-1) Δ 2 Y -1 + P (P-1) (P-2) Δ 3 Y -1 + P (P-1) (P-2) (P-3) Δ 4 Y -2 2! 3 ! 4 ! Where P=X – X /h

4. X Y Δ Δ 2 Δ 3 Δ 4 X -2 Y -2 ΔY -2 X -2 Y -1 Δ 2 Y -2 ΔY -1 Δ 3 Y -2 X Y Δ 2 Y -1 Δ 4 Y -2 ΔY Δ 3 Y -1 X 1 Y 1 Δ 2 Y ΔY 1 X 2 Y 2

5. Gauss Backward Central Difference Formula Y= f(x) = P n (x) = Y + PΔY + P (P+1) Δ 2 Y -1 + P (P+1) (P+2) Δ 3 Y -1 + P (P+1) (P+2) (P+3) Δ 4 Y -2 2! 3 ! 4 ! Where P=X – X /h

6. X Y Δ Δ 2 Δ 3 Δ 4 X -2 Y -2 ΔY -2 X -2 Y -1 Δ 2 Y -2 ΔY -1 Δ 3 Y -2 X Y Δ 2 Y -1 Δ 4 Y -2 ΔY Δ 3 Y -1 X 1 Y 1 Δ 2 Y ΔY 1 X 2 Y 2