This document discusses polynomial interpolation and fitting methods in MATLAB. It provides examples of: - Finding the roots of a polynomial using the roots() function. - Using polyfit() to find the coefficients of a polynomial that fits a set of data points. - Using interpl() to perform linear, spline, and piecewise cubic interpolation between data points. - Creating mesh and surface plots by generating a grid in the x-y plane and calculating the z-values at each point.

1. BY
Uday Saikia

7. >> p=[1 -12.1 40.59 -17.015 -71.95 35.88]
>> r=roots(p)
r=
6.5000
4.0000
2.3000
-1.2000
0.5000

12. 6x-2

13. p=polyfit(x,y,n)
here p=A vector of the co-efficients of
the polynomial that fits the
data
co-
x=A vector with the horizontal
ordinate of the data points
y= A vector with the vertical
co-ordinate of the data points
n=Degree of polynomial

14. Here,
‘nearest’ : returns the value of the
data point that is nearest to the
yi = interpl (x, y, xi, ‘method’) interpolated point
‘linear’ : uses linear spline
interpolation
‘spline’ : uses cubic spline
interpolation
yi = It is Interpolated value
‘pchip’ : uses piecewise cubic Hermite
interpolation
x = It is a vector with horizontal co-ordinate of the input data
points
y = It is a vector with vertical co-ordinate of the input data points
xi = Horizontal co-ordinate of the interpolation point

16. x
0
1
2
y
1.0
-0.6242 -1.4707
3
4
5
3.2406
-0.7366 -6.3717

17. >> x=[0:1.0:5];
y=[1.0 -0.6242 -1.4707 3.2406 -0.7366 -6.3717];
xi=[0:0.1:5];
yilin=interpl(x,y,xi,'linear');
yispl=interpl(x,y,xi,'spline');
yipch=interpl(x,y,xi,'pchip');
yfun=1.5.^xi*cos(2*xi);
subplot(1,3,1)
plot(x,y,'o'xi,yfun,xi,yilin,'--');
subpolt(1,3,2)
plot(x,y,'o',xi,yfun,xi,yispl,'--');
subplot(1,3,3)
plot(x,y,'o',xi,yfun,xi,yipch,'--')

22. Mesh & Surface plots are created in three steps:
*create a grid in the x-y plane
*calculate the value of z at each point of the grid
*create the plot

24. >> x=-1:0.1:3;
>> y=1:0.1:4;
>> [X,Y]=meshgrid(x,y);
>> Z=X.*Y.^2./(X.^2+Y.^2);
>> mesh(X,Y,Z)
>> xlabel('x');
>> ylabel('y');
>> zlabel('z');