Question

must be done in MATLAB

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). ( 4,5), (7, 3), (12, 20) Output: (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 (h=x,-x,..) using Lagrange interpolation form Input: (copy and paste the MATLAB or Scilab Lagrange.m subroutine

Answer 1

Answer:

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 b) Below plot is for data poin: (1,5) (0,813,-10) 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

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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) %% 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);