1. Submitting to -
Naveen Kumar S B
Science & Humanities
Presented by -
Gowtham CR – PES1201801581
Nithin Chandra R – PES1201801340
Branch & Section – EEE 4’A
2. Curve Fitting is the process of constructing a curve, or
mathematical function, that has the best fit to a series of
3. Matrix is one of the most thought and
used form or method to simplify such
It’s the same case here, we used
matrix method which includes matrix
Matrix method is also helpful in storing
the inputs(co-ordinate points) in the
form of matrix.
4. To find the curve equation using the inputs(co-ordinate points), it
need’s users effort to solve for it each and every time.
So, coding it wouldn't just nullify the users efforts but also he/she
can visualize the curve by plotting it .
The code is user friendly which even permits the user to choose the
degree of polynomial which should less them number of inputs.
More the no.of inputs more close it is to the expected equation.
5. Any polynomial of order ‘n’ can be expressed as:
Y = a*xn+ b*x(n-1) + c*x(n-2) + ….. + k*x(n-(n-1) + C
In here, by substituting the value of ‘x’ and ‘Y’ accordingly, We find a
set of linear equations with constants a, b, c,….., k, C to be unknowns.
Solving for those and
substituting them back to the
general equation, we could find
the expected equation.
6. We’ve used matrices and inverse method to find the best fitting curve –
Let’s consider the degree of polynomial m=3. And the number of co-
ordinate points, which should be greater than or equal to m+1, to be
We know that any cubic equation should be of the form
Y = Ax3+Bx2+Cx+D.
Substituting ‘x’ and ‘Y’ values of each of the co-ordinate points. We get
5 equations each with 4 common unknowns A, B, C and D.
7. Now we use linear algebra to find these unknowns by inserting the
values of ‘Y’ in a matrix and the co-efficient of A, B, C and D in another
Let's, name these matrixes Q and P respectively.
P*A = Q, wherein A is the matrix of Constants.
A = inverse (P)*Q || if inverse of P exists or else
A = (inverse (transpose (P)*(P)))*(transpose (P)*Q) || in which
left inverse for the matrix ‘P’ is given by (inverse (transpose
We got all the constants which are placed back in the general
The required polynomial if found out and it has been plotted in the
8. Advantages -
As mentioned before reduces human efforts and user can view the
equation’s graphical representation.
Could be used any number of times and for any degree of
Could be used to convert any non-polynomial( exponential,
trigonometric, etc..,) into a approximate polynomial function.
Non-polynomial output can’t be obtained.
11. For the input
a. Degree of the Polynomial (m) = 3
b. Number of co-ordinate points (n) = 4
c. (0, -12), (1, -12), (-1, -6), (2, 0) are the co-ordinate points which are
in (x, y) format.