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Lagrange Interpolation In this livescript, you will learn how To use Lagrange interpolation approximate functions Consider two points (x_{0},y_{0}) and (x_{1},y_{1}) (a) Show that linearly interpolating between these two points yields the linear relationship y=ax+b where a=\frac{y_{1}-y_{0}}{x_{1}-x_{0}} b=\frac{y_{0}(x_{1}-x_{0})-(y_{1}-y_{0})x_{0}}{x_{1}-x_{0}} (b) Show that this may be rearranged into the form y=y_{0}\Big(\frac{x-x_{1}}{x_{0}-x_{1}}\Big)+y_{1}\Big(\frac{x-x_{0}}{x_{1}-x_{0}}\Big) (c) Consider the set of three points \{(x_{0},y_{0}),(x_{1},y_{1}),(x_{2},y_{2})\} . Repeat parts (a) and (b) and show that the quadratic interpolating polynomial is given by y=y_{0}\Bigg(\frac{(x-x_{1})(x-x_{2})}{(x_{0}-x_{1})(x_{0}-x_{2})}\Bigg)
+
y_{1}\Bigg(\frac{(x-x_{0})(x-x_{2})}{(x_{1}-x_{0})(x_{1}-x_{2})}\Bigg)
+
y_{2}
\Bigg(\frac{(x-x_{0})(x-x_{1})}{(x_{2}-x_{0})(x_{2}-x_{1})}\Bigg) It turns out that in general, we may write the interpolating polynomial in the form p(x)=\sum^{N}_{i=0}{y_{i}L_{i}(x) Equation 1. where L_{i}(x)=\prod^{N}_{j=0,j\neq i}{\frac{x-x_{j}}{x_{i}-x_{j}}}=\frac{x-x_{0}}{x_{j}-x_{0}}\cdots\frac{x-x_{i-1}}{x_{i}-x_{i-1}}\frac{x-x_{i+1}}{x_{i}-x_{i+1}}\cdots\frac{x-x_{N}}{x_{i}-x_{N}} Essentially, what this says is that the Lagrange basis \{L_{i}\} is 1 at the i^{\text{th}} nodal point and 0 everywhere else. This is what is known as the Lagrange interpolation property . To implement this in MATLAB, the following piece of code determines the lagrange basis polynomials x = 1;
xs = [0,1,4];
i = 1;
L = 1;
for j = 1:length(xs)
if j~=i
L = L*(x-xs(j))/(xs(i)-xs(j));
end
end
L (d) Run this piece of code and understand each line of code does. (e) Generalise the code so that it can take a vector \texttt{x} as an input. To determine how this works, we’ll consider the test function f(x)=e^{x} And interpolate it with 2 points between 0\leq x \leq 1 . The function values at the nodes is given by nodes = linspace(0,1,2);
f = exp(nodes); For convinence, the previous piece of code is placed in a MATLAB function \texttt{lagrange\_L(i,x\_nodes,x\_points)} . Hence the interpolating polynomial is given by x1 = linspace(0,1,100);
y1 = 0;
for l = 1:length(nodes)
y1 = y1+f(l)*lagrange_L(l,nodes,x1);
end
plot(x1,y1)
hold on
plot(x1,exp(x1))
xlabel(‘x’)
ylabel(‘f(x)’)
hold off The error is therefore Error = abs(y1′-exp(x1));
plot(x1,Error)
xlabel(‘x’)
ylabel(‘|Error|’) (e) Modify the code to use 3 and 4 interpolating nodes between 0\leq x \leq 1 . Does the accuracy of the approximation increase?
manual code ready 0.4 variable L 0 1 1 13 figure ec6c804b-cd3f-40e5-99d9-14abad56e3c2 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 560 420 11 12 13 14 15 16 11 23 24 25 26 27 28 figure d5c7c1b7-5fac-4526-9731-569c73c5c2c9 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×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 560 420 18 19 20 18 30 31 32 true false x = 1; 0 25 25 false false xs = [0,1,4]; 1 26 26 false false i = 1; 2 28 28 false false L = 1; 3 29 29 false false for j = 1:length(xs)
if j~=i
L = L*(x-xs(j))/(xs(i)-xs(j));
end
end 4 31 35 false true L 5 37 37 0 true false nodes = linspace(0,1,2); 6 45 45 false true f = exp(nodes); 7 46 46 true false x1 = linspace(0,1,100); 8 49 49 false false y1 = 0; 9 50 50 false false for l = 1:length(nodes)
y1 = y1+f(l)*lagrange_L(l,nodes,x1);
end 10 52 54 false false plot(x1,y1) 11 56 56 1 false false hold on 12 57 57 1 false false plot(x1,exp(x1)) 13 58 58 1 false false xlabel(‘x’) 14 59 59 1 false false ylabel(‘f(x)’) 15 60 60 1 false true hold off 16 61 61 1 true false Error = abs(y1′-exp(x1)); 17 64 64 false false plot(x1,Error) 18 65 65 2 false false xlabel(‘x’) 19 66 66 2 false true ylabel(‘|Error|’) 20 67 67 2
2020-03-27T06:50:57Z 2020-04-09T07:21:22Z
application/vnd.mathworks.matlab.code MATLAB Code R2019b
9.7.0.1183724 d006df74-34ff-466b-93db-95ab7342888f
9.7.0.1296695
R2019b
Update 4
Jan 20 2020
3546228467