Question

2. Create a main program that calls the subroutine created on problem 1 and compare results using the following data sets: b. 1 5), (0, 8), (3,-10) С. (-10,-2), (45), (73), (12, 20) t: (copy and paste the output in the following box) Use MATLAB or Scilab to solve the following problems 1. Create a MATLAB subroutine called Lagrange.m that receives two set data points, x and y and plots the curve by interpolating the missing points (hEX-Xi-1) using Lagrange interpolation form. Input: (copy and paste the MATLAB or Scilab Lagrange.m subroutine

Answer 1

2) Data sets are compared using the below program close all clc clear all: 6% Given input data points pointX [1,4]: pointY-13,7); 966 Missing points x-2,4]: %% Interpolating using the Sub routine y lagrange(x,pointX,pointY); %% Given input data points pointX-[-1,0,3]; pointY [5,8,-10]; 9696 Missing points figure; %% Interpolating using the Sub routine y lagrange(x,pointxX,pointY); %% Given input data points pointX-I-10,4,7,12]; pointY-[-2,5,3,20]; 966 Missing points figure; %% Interpolating using the Sub routine y lagrange(x,pointX,pointY);

Below plots shows the data set before interpolation and after interpolation a) Below plot is for data point (1,3) (4) original -after Inter poation 6.5 5.5 4.5 3.5 2.6 3 5 o) Below plot is for data port (-1,5) O8X3.-LO) oniginal ter Inter polatic 10 1 05 05 2 25 3 c)below is the plot fort-10,-2) (4,5) (7,3) (12,20 20 original _after Inter polation 15 10

1) Below code is subroutine lagrange, Save this subroutine as lagrange.m. and call the function in the main program. explanation of the code is in the comments. function y=lagrange(x,point,pointy) 9696 In this function x is the points to be calculted, y is the interpolated value %% calculate the input size n-size(pointx,2); %% Generate the initial values of the x L=ones(n, size(x2); 9696 Calcaulate the missing points using legranges interpolation formule for i=1:n for j=1:n if (i-j) L(i,)-L(i:).* (x-pointx)/(pointx0)-pointx); en en for i=1:n %%Sorting X and Y X=(x points), Y-[y pointyl; [sortedX, sortindex] = sort(X) sortedY = Y(sort!ndex) %% Plot the graph plot pointx,pointy, Color,red') hold on; plot sortedX,sortedY,Color,blue'); hold off legend('original,'after Inter polation);