Question

can anyone help me in writing Program in Matlab for Lagrange interpolation . which should take data from user in the form of vectors (abscissa and ordinate) and return the coefficients of Lagrange interpolating Polynomials.

Answer 1

lagran.m

1. MATLAB stores polynomials by storing their coefficients in a row vector ( 3 x 1 matrix)
Hence the polynomial x2 + 2x +3 would be stored as the vector [1 2 3]

» P = [1 2 3]
P =
1 2 3

2. MATLAB has a several routines that allows one to manipulate polynomials.
We can evaluate polynomials at a particular point with the command polyval
The following evaluates the polynomial with coefficients stored in P above at the value x = 2:

» polyval(P,2)
ans =
11

3. The conv command can be used to multiply two polynomial. For example, to multiply the above polynomial by (x + 1) -- i.e. to compute (x2 + 2x + 3) (x + 1):

» Q = [1 1]
Q =
1 1

» conv(P,Q)
ans =
1 3 5 3
( The result is thus x3+ 3x2 + 5x + 3. )

4. The MATLAB Symbolic Toolbox also has some commands for manipulating polynomials symbolically. The poly2sym command converts a vector of coefficients to a symbolic polynomial.

» syms x
» poly2sym(P,x)
ans =
x^2+2*x+3

5. To find the polynomial of degree n that passes through n + 1 data points we can use polyfit.
» help polyfit

To find the polynomial passing through the points in Example 4.4, page 200:
» X = [1 2 3 5]
» Y = [1.06 1.12 1.34 1.78]
» P = polyfit(X,Y,3)
P =
-0.0200 0.2000 -0.4000 1.2800



Thus the polynomial fitting these points is

-0.02x3 +0.2x2-0.4x +1.28.

You can see that MATLAB produces the correct coefficients agreeing with your text.

Answer 2

thanks :)

Answer 3

you welcome