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Aid to homeword 3.1 Problem 1

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Matthew Ellison
2018-10-10 12:27:33 -04:00
parent 92e796df06
commit 2a245cbef2
2 changed files with 90 additions and 0 deletions
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Homework/Homework311.m Normal file
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%This is a script to do the homework for 3.1 problem1
pkg load symbolic;
syms x;
x_list = [0, 0.6, 0.9];
xValue = 0.45;
%Part a
y_list = cos(x_list);
f = cos(x);
disp('a:')
[P01, P12, P02] = LagrangePolynomialSymbolic(x_list, f);
fEval = double(subs(f, xValue));
pEval = double(subs(P01, xValue));
disp('Error:')
disp(['|f(x) - P01(x)| = |' num2str(fEval, '%9.9g') ' - ' num2str(pEval, '%9.9g') '| = ' num2str(abs(fEval - pEval), '%9.9g')])
pEval = double(subs(P02, xValue));
disp(['|f(x) - P02(x)| = |' num2str(fEval, '%9.9g') ' - ' num2str(pEval, '%9.9g') '| = ' num2str(abs(fEval - pEval), '%9.9g')])
%Part b
y_list = sqrt(1 + x_list);
f = sqrt(1 + x);
disp('')
disp('')
disp('b:')
[P01, P12, P02] = LagrangePolynomialSymbolic(x_list, f);
fEval = double(subs(f, xValue));
pEval = double(subs(P01, xValue));
disp('Error:')
disp(['|f(x) - P01(x)| = |' num2str(fEval, '%9.9g') ' - ' num2str(pEval, '%9.9g') '| = ' num2str(abs(fEval - pEval), '%9.9g')])
pEval = double(subs(P02, xValue));
disp(['|f(x) - P02(x)| = |' num2str(fEval, '%9.9g') ' - ' num2str(pEval, '%9.9g') '| = ' num2str(abs(fEval - pEval), '%9.9g')])
%Part c
y_list = log(x_list + 1);
f = log(x + 1);
disp('')
disp('')
disp('c:')
[P01, P12, P02] = LagrangePolynomialSymbolic(x_list, f);
fEval = double(subs(f, xValue));
pEval = double(subs(P01, xValue));
disp('Error:')
disp(['|f(x) - P01(x)| = |' num2str(fEval, '%9.9g') ' - ' num2str(pEval, '%9.9g') '| = ' num2str(abs(fEval - pEval), '%9.9g')])
pEval = double(subs(P02, xValue));
disp(['|f(x) - P02(x)| = |' num2str(fEval, '%9.9g') ' - ' num2str(pEval, '%9.9g') '| = ' num2str(abs(fEval - pEval), '%9.9g')])
%Part d
y_list = tan(x_list);
f = tan(x);
disp('')
disp('')
disp('d:')
[P01, P12, P02] = LagrangePolynomialSymbolic(x_list, f);
fEval = double(subs(f, xValue));
pEval = double(subs(P01, xValue));
disp('Error:')
disp(['|f(x) - P01(x)| = |' num2str(fEval, '%9.9g') ' - ' num2str(pEval, '%9.9g') '| = ' num2str(abs(fEval - pEval), '%9.9g')])
pEval = double(subs(P02, xValue));
disp(['|f(x) - P02(x)| = |' num2str(fEval, '%9.9g') ' - ' num2str(pEval, '%9.9g') '| = ' num2str(abs(fEval - pEval), '%9.9g')])
%Cleanup your variables
clear P01 P12 P02 f fEval pEval x xValue x_list y_list

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Homework/LagrangePolynomialSymbolic.m Normal file
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function [ P01, P12, P2 ] = LagrangePolynomialSymbolic(x_list, f)
syms x;
format long;
warning('off','OctSymPy:sym:rationalapprox');
%Evaluate P0,1
%P01 = (((x - x_list(2))/(x_list(1) - x_list(2))) * double(subs(f, x_list(1)))) + (((x - x_list(1))/(x_list(2) - x_list(1))) * double(subs(f, x_list(2))))
P01x = (double(subs(f, x_list(1)))/(x_list(1) - x_list(2))) + (double(subs(f, x_list(2)))/(x_list(2) - x_list(1)));
P01c = ((double(subs(f, x_list(1)))/(x_list(1) - x_list(2))) * -x_list(2)) + ((double(subs(f, x_list(2)))/(x_list(2) - x_list(1))) * -x_list(1));
disp(['P01 = ' num2str(P01x, '%9.9g') 'x + ' num2str(P01c, '%9.9g')])
P01 = (P01x * x) + P01c;
%Evaluate P1,2
%P12 = (((x - x_list(3))/(x_list(2) - x_list(3))) * double(subs(f, x_list(2)))) + (((x - x_list(2))/(x_list(3) - x_list(2))) * double(subs(f, x_list(3))))
P12x = (double(subs(f, x_list(2)))/(x_list(2) - x_list(3))) + (double(subs(f, x_list(3)))/(x_list(3) - x_list(2)));
P12c = ((double(subs(f, x_list(2)))/(x_list(2) - x_list(3))) * -x_list(3)) + ((double(subs(f, x_list(3)))/(x_list(3) - x_list(2))) * -x_list(2));
disp(['P12 = ' num2str(P12x, '%9.9g') 'x + ' num2str(P12c, '%9.9g')])
P12 = (P12x * x) + P12c;
%Evaluate P2
%P2 = (P2x * x) + P2c;
P2x2 = (P01x - P12x) / (x_list(1) - x_list(3));
P2x = ((P01c) + (P01x * -x_list(3)) - ((P12x * -x_list(1)) + (P12c))) / (x_list(1) - x_list(3));
P2c = ((P01c * -x_list(3)) - (P12c * -x_list(1))) / (x_list(1) - x_list(3));
disp(['P02 = ' num2str(P2x2, '%9.9g') 'x^2 + ' num2str(P2x, '%9.9g') 'x + ' num2str(P2c, '%9.9g')])
P2 = (P2x2 * x^2) + (P2x * x) + P2c;
end