QUIZ 7

1. We have given the following MATLAB code to evaluate the Lagrange polynomial,

function [C,L]=lagran(X,Y)

%Input - X is a vector that contains a list of abscissas

% - Y is a vector that contains a list of ordinates

w=length(X);

n=w-1;

L=zeros(w,w);

for k=1:n+1

V=1;

for j=1:n+1

if k~=j

V=conv(V,poly(X(j)))/(X(k)-X(j));

end

end

L(k,:)=V;

end

C=Y*L;

where

The poly command creates a vector whose entries are the coefficients of a polynomial with specified roots.

>>P=poly(2)

>> 1 -2

>>Q=poly(3)

>> 1 -3

The conv command produces a vector whose entries are the coefficients of a polynomial that is the product of two other polynomials.

>>conv(P,Q)

>> 1 -5 6 %Thus the product of P(x) and Q(x) is x^2-5x+6

And

>> X=[1 2 3 5]

>> Y=[1.06 1.12 1.34 1.78]

>> [C,L]=lagran(X,Y)

C = -0.0200 0.2000 -0.4000 1.2800

L =

-0.1250 1.2500 -3.8750 3.7500

0.3333 -3.0000 7.6667 -5.0000

-0.2500 2.0000 -4.2500 2.5000

0.0417 -0.2500 0.4583 -0.2500

Describe the meaning of the vector C.