Interpolation

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Interpolation

• Lagrangian Interpolation

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Lagrangian interpolating polynomial
This is also used for unequally spaced points.
This is a reformulation of Newtons divide
difference interpolating polynomial and it avoids
the calculation of divide differences. It is of
the form
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Here equation (1) represents the Lagrangian
Interpolating polynomial and (2) represents
Lagrangian function.
Note-
Example
Find f(2.8) using Lagrangian Interpolating
polynomial for the data
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Ans-
For the given data, the Lagrangian Interpolating
Polynomial is
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Finite Differences Forward differences
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Forward difference Table-







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Example-
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Forward difference Table-







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Newtons Forward difference Interpolation
Formula -
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Example
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Forward difference Table-







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Finite Differences Backward differences
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Backward difference table







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Example-
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Backward difference table







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Newtons Backward difference Interpolation
Formula -
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Example
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Backward difference table







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Thank You ALL

• Presented by
• Boina Anil Kumar
• Asst.Prof in Mathematics
• MITS, Rayagada.
• Odisha, India
• E-mail anil.anisrav_at_gmail.com
• Visit at http//www.mits.edu.in/academics.phpfac
  ulty_BSH-tab

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Thank You ALL
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