Newton’s Forward Interpolation Formula with MATLAB Example

13 May

Newton’s Forward Interpolation Formula with MATLAB Example :

Interpolation:

Introduction:

In everyday life, sometimes we may require to find some unknown value with the given set of observations. For example, the data available for the premium, payable for a policy of Rs.1000 at age x, is for every fifth year. Suppose, the data given is for the ages 30, 35, 40, 45, 50 and we are required to find the value of the premium at the age of 42 years, which is not directly given in the table. Here we use the method of estimating an unknown value within the range with the help of given set of observation which is known as interpolation.

Definition of interpolation:

Given the set of tabular values (x0, y0), (x1, y1),…,(xn, yn) satisfying the relation y=f(x) where the explicit nature of f(x) is not known, it is required to find a simpler function say ф(x), such that f(x) and ф(x) agree at the set of tabulated points. Such a process is called as interpolation.

If we know ‘n’ values of a function, we can get a polynomial of degree (n-1) whose graph passes through the corresponding points. Such a polynomial is used to estimate the values of the function at the values of x.

We will study two different interpolation formula based on finite differences, when the values of x are equally spaced. The first formula is:

Newton’s forward difference interpolation formula:

The formula is stated as:

1

Where ‘a+ph’ is the value for which the value of the function f(x) is to be estimated. Here ‘a’ is the initial value of x and ‘h’ is the interval of differencing.

Question:

Table gives the distance between nautical miles of the visible horizon for the given height in feet above the earth surface.  Find the value of y when x= 218 feet .

newtons forward interpolation formula

newtons forward interpolation formula

MATLAB program for Newtons forward interpolation formula :

newtons forward interpolation formula 1

newtons forward interpolation formula 1

newtons forward interpolation formula 2

newtons forward interpolation formula 2

You may also like:

 

About these ads

One Response to “Newton’s Forward Interpolation Formula with MATLAB Example”

  1. chijioke February 22, 2014 at 3:06 AM #

    good one. thanks

    Like

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

Join 79 other followers

%d bloggers like this: