Introduction to Interpolation

  • Newton Interpolation Formula for Unequal Intervals

    When the values of the independent variable occur with unequal spacing the formula discussed earlier is no more applicable. In this situation another formula which is based on divided difference is used. Before presenting the formula let us first discuss about what are divided differences. Divided Differences: Let the values of the independent variable are […]

  • Examples of Newton Interpolation

    Example No 1: The following supply schedule gives the quantity supplied in hundreds of a product at prices in rupees: 80 90 100 110 120 25 30 42 50 68   Interpolate, what will be the quantity supplied of the product at a price Dollor 85. Solution: Constructing the difference table first. THE DIFFERENCE TABLE […]

  • Newton Interpolation Formula

    A number of different formulae were given by Newton, however, two of these formulae are more common. One of these formulae is used when the independent variable assumes values with equal interval while the other is applicable when the interval is not equal. The first formula is referred to as “Newton’s formula for equal interval”, […]

  • Examples of Lagrange Interpolation

    Example No 1: Interpolate the value of the function corresponding to , using Lagrange’s Interpolation formula from the following set of data: 2 3 5 8 12 10 15 25 40 60   Solution: Using formula of Lagrange Interpolation, we have Now simplify the brackets terms and write them in brackets with their proper sign […]

  • Lagrange Interpolation Formula

    Lagrange’s formula is applicable to problems where the independence variable occur with equal and unequal intervals, but preferably this formula is applied in a situation where there are unequal intervals in the given independence series. Let the values of the independence variables are given as   etc., and the corresponding values of the function (dependent variable) […]

  • Introduction to Interpolation

    The time series data which is recorded after regular or irregular interval of time consists of values of a phenomenon at a certain point in time or the values of some hypothetical function corresponding to a few values of independent variable are not sufficient to provide information regarding the values of the same phenomenon in […]