fall'17

1. Linear Curve Fitting Along With
Gauss Backward.

2. Shanawaz Ahamed 2016-1-60-103
Muhsena Shafiquie 2016-1-60-115
Tahmid Ahmed 2016-1-68-007

3. Outlines:
 Concept of Curve Fitting & Interpolation Methods.
 Linear Curve Fitting Method.
 Gauss Backward Interpolation.
 Applications.
 Code implication.
 Conclusion.

4. Linear Curve Fitting Method.
General Equation is , f(x) = bx + a.
Here,
b= Co-efficient of x.
a= Constant.
It is actually straight line.
𝑏 =
𝑛∑𝑥𝑖𝑦𝑖−∑𝑥𝑖 ∑𝑦𝑖
𝑛 ∑ 𝑥𝑖2−(∑ 𝑥𝑖)2 ;
𝑎 =
∑𝑦𝑖
𝑛
− 𝑏
∑𝑥
𝑛
;

5. Gauss Backward Interpolation.
 Here for any given value of x, we calculate the value of y.
 Formula,
y(x)= 𝑦ℴ + 𝑢∆𝑦 − 1 +
𝑢 𝑢+1
2!
∆2
𝑦 − 1 +
𝑢−1 𝑢 𝑢+1
3!
∆3
𝑦 − 2 + ⋯ ;
 𝑢 =
𝑥−𝑥𝑛
ℎ
;

6. Code Implication
When Relationship Linear.
1) Select the length .
2) Input Value of x and y.
3) Calculate summation of x, y, 𝑥2 and
𝑥 ∗ 𝑦.
4) Calculate a and b from equation.

7. Code Implication
Gauss Backward interpolation.
1) Input all value of x in linear equation.
2) Get all the value of y.
3) Take input of x.
4)Calculate ∆𝑦, ∆2
𝑦, ∆3
𝑦, ∆4
𝑦 …
5) Calculate Result by using equation.

8. Conclusion.
 It’s a major sector of modern science era.
 Nowadays we use many real life applications of numerical method.
 We can know all approximate solutions.
 IT helps to find better algorithms that cause less errors.