Lagrange Interpolation Calculator

Lagrange Interpolation Calculator is a free online tool that displays the interpolating polynomial, and its graph when the coordinates are given. BYJU’S online Lagrange interpolation calculator tool makes the calculation faster, and it displays the polynomial and graph in a fraction of seconds.

How to Use the Lagrange Interpolation Calculator?

The procedure to use the Lagrange interpolation calculator is as follows:
Step 1: Enter the coordinate values in the respective input field
Step 2: Now click the button “Submit” to get the polynomial
Step 3: Finally, the interpolating polynomial and the graph will be displayed in the new window

What is Meant by Lagrange Interpolation?

In Mathematics, interpolation is defined as the estimation of the value within the known sequence values. Lagrange polynomial interpolation is defined as the process of determining the values within the known data points. Lagrange interpolating polynomial is a method of calculating the polynomial equations for the corresponding curves that have coordinates points. This method provides a good approximation of the polynomial functions. Lagrange polynomial is a polynomial with the lowest degree that assumes each value to the corresponding values. When applying Lagrange interpolation for the given set of points with unequal values, the function coincides with each point.

Finding Lagrange Polynomial

To find the Lagrange interpolating polynomial, the following formula is used.

$P(x) = \sum_{j=0}^{n}y_{j}\left ( \prod_{i=0,i\neq j }^{n}\frac{X – x_{i}}{x_{j}-x_{i}} \right )$

With the coordinates (x0, y0), …., (xn, yn) and distinct xi.

For example, if we take the known data points such as (2, 3), (4, 5), (5, 7), and (7, 9) be the known data values, then the Lagrange interpolating polynomial is given by:
-(2x3/15) + (9x2/5) – (91x/15) + 9