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Home » Articles » LESSON NOTES (Mathematics) » High School level


NUMERICAL METHODS NMDLI104AR

LINEAR INTERPOLATION

Consider the following diagram:

Let M be the slope of the straight line PQ then

M = [f(b) – f(a)]/ (b – a) ------------------- (I)

Also

M = [f(c) – f(a)]/ (c – a)

Since both are the value of the slope M then [[f(b) – f(a)]/ (b – a)] = [[f(c) – f(a)]/ (c – a)] then by making subject f(c) the equation will become:

 

  this is called linear interpolation... Read more this article

 

Application of linear interpolation:

 

Example #1:

The function f(x) takes the following values:

  X

    1

    2

  3

F(X)

   0.5

  0.33

 0.25

Using linear interpolation find the value of 2.2.

Solution:

From the table above 2.2 is found between 2 and 3, f (2) and f (3) then from the formula

F (b) = 0.25, F (a) = 0.33, b = 3, a= 2 and c is the given number that is 2.2 so we need to find F (2.2),

By substitution from the formula F (2.2) = 0.314.

There fore the value of 2.2 is 0.314

 

Example #2

Given that e1.25 = 3.4903 and e1.26 = 3.5254 find e1.257 by using linear interpolation.

Solution:

From the question x = 1.25 and 1.26 then in the table will be

       X             

    1.25

     1.26

     F (X)

   3.4903

   3.5254

From the above 1.257 lies between 1.25 and 1.26 then using the formula

F (b) = 3.5254, F (a) = 3.4903, a = 1.25, b= 1.26 and c is the given number that is 1.257 then we need to find F (1.257).

By substitution in the linear interpolation the answer will be 3.5149

There fore e1.257 = 3.5149.

 

Example #3

If sin 35˚ = 0.5736 and sin 40˚ = 0.6428 find sin 37˚ by using linear interpolation.

Solution:

      X

    35

       40

   F (X)

   0.5736

   0.6428

37˚ lies between 35˚ and 40˚ then from the equation F (b) = 0.6428, F (a) = 0.5736, b = 40, a = 35 and c is the given angle that is 37˚ then we need to find F (37).

After substitution to linear interpolation the value of sin 37˚ is 0.60128

Qn: Given that log (1.96) = 0.2923 and log (1.97) = 0.2945, using linear interpolation find the number for which log (x) = 0.2935.

 

--------------END OF LINEAR INTERPOLATION ---------------------

Category: High School level | Added by: Admin (07/Aug/2016) | Author: Yahya Mohamed E W
Views: 460 | Tags: NMDLI104AR, numerical methods, interpolation. linear | Rating: 0.0/0
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