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Netwon Interpolation In this livescript, you will learn how To use Netwon interpolation approximate functions For a set of datapoints (x_{0},f(x_{0})),\ldots,(x_{k},f(x_{k})) The Newton interpolating polynomial is defined as f_{n}(x)=\sum^{k}_{i=0}{b_{i}N_{i}(x)} where N_{i}}(x) is defined as the product N_{i}(x)=\prod^{i-1}_{\ell=0}{(x-x_{\ell})}=(x-x_{0})\cdots(x-x_{i-1}) For the rest of this livescript, we’ll consider approximating the function f(x)=|\text{sin}(x^{2})| at the sampling points x=\{-1,-1/3,1/3,1\} x = linspace(-1,1,4)
f = abs(sin(x.^2))
figure
plot(linspace(-1,1,100),abs(sin(linspace(-1,1,100).^2)));
hold on
plot(x,f,’.’,’MarkerSize’,15)
xlabel(‘x’)
ylabel(‘f(x)’)
hold off Newton basis polynomials So let’s write a piece of code that computes each N_{i}}(x) at some point x . The inputs of this function will therefore need to be The x coordinate. The order i . The interpolation points x_{\ell} . Since there are a known number of computations to be made, we can use a for loop. The idea behind using a loop here is that initially, we set N_{i,\text{Step 0}}=(x-x_{0}) Then going into the loop we multiply out initial condition by (x-x_{1}) , giving N_{i,\text{Step 1}}=(x-x_{0})(x-x_{1}) For the next iteration, we multiply by (x-x_{2}) , which gives N_{i,\text{Step 2}}=(x-x_{0})(x-x_{1})(x-x_{2}) Repeating this process until we reach (x-x_{i-1}) would therefore give us the desired result. Here we have a piece of code that does this for N_{2} at x=1 , which is sampled at the points \{1,2,3,4,5\} . x = 1;
i = 2;
xpoints = [1,2,3,4,5];
Ni = 1;
for l=1:i
Ni = Ni*(x-xpoints(l));
end
Ni (a) Convert this piece of code into a function. Divided Differences As for the divided differences b_{i} , our inputs will need to be The order i . The interpolation points x_{\ell} and y_{\ell} . For the coefficients b_{i} , the n^{\text{th}} divided difference is given by f[x_{n},\ldots,x_{0}]=\frac{f[x_{n},x_{n-1},\ldots,x_{1}]-f[x_{n-1},x_{n-2},\ldots,x_{0}]}{x_{n}-x_{0}} which we may represent graphically by What this is saying is that the 3^{\text{rd}} divided difference relies on two 2^{\text{nd}} divided difference, which itself relies on three 1^{\text{st}} divided differences. This recursive definition means that we need to construct our n^{\text{th}} divided difference from the 1^{\text{st}} divided difference upwards. (b) Determine the 1^{\text{st}} , 2^{\text{nd}} , 3^{\text{rd}} , and 4^{\text{th}} divided differences of Eq. (1). So let’s then look at constructing the 1^{\text{st}} divided difference using MATLAB. Since we know our end point, we’ll use a for loop, then a piece of code that determines the 1^{\text{st}} divided differences f[x_{j},x_{j+1}]=\frac{f(x_{j})-f(x_{j+1})}{x_{j}-x_{j+1}} is xpoints = linspace(-1,1,4);
ypoints = abs(sin(xpoints.^2));
f0 = ypoints;
f1 = zeros(1,length(f0)-1);
for j=1:length(f0)-1
f1(j) = (f0(j)-f0(j+1))/(xpoints(j)-xpoints(j+1));
end
f1 (c) Run the piece of code and check that the code produces the same result. (d) Modify the code to construct the second divided differences. So wrapping the piece of code in a second for loop to determine the (i+1)^{\text{st}} divided difference from the i^{\text{th}} divided difference, we have xpoints = linspace(-1,1,4);
ypoints = abs(sin(xpoints.^2));
f1 = zeros(length(xpoints),length(xpoints));
f1(1,:) = ypoints;
for i=1:length(xpoints)-1
for j=1:length(f1)-i
f1(i+1,j) = (f1(i,j)-f1(i,j+1))/(xpoints(j)-xpoints(j+i));
end
end
f1
disp(f1(end,1)) (e) Run the piece of code and see if it matches the your result in (a). (f) Convert this piece of code into a function. And so, the Newton interpolating polynomial is given by xpoints = linspace(-1,1,4);
ypoints = abs(sin(xpoints.^2));
x = linspace(-1,1,100);
f=0;
for i = 0:length(xpoints)-1
f = f+divdiff(xpoints(1:i+1),ypoints(1:i+1)).*newton_N(x,i,xpoints);
i
end
a = polyfit(xpoints,ypoints,length(xpoints)-1);
fit = polyval(a,x);
plot(xpoints,ypoints,’.’,’MarkerSize’,15)
hold on
plot(x,fit,’x-‘)
plot(x,f)
hold off
plot(x,abs(fit-f)) For convenience, the Newton basis polynomials are determined using the function \texttt{newton\_N} and the divided differences in the function \texttt{divdiff} .
manual code ready 0.4 matrix x 1×4 1 4 double -1.0000 -0.3333 0.3333 1.0000
double double [[{“value”:”{\”value\”:\”-1.0000\”}”},{“value”:”{\”value\”:\”-0.3333\”}”},{“value”:”{\”value\”:\”0.3333\”}”},{“value”:”{\”value\”:\”1.0000\”}”}]] 1 matrix f 1×4 1 4 double 0.8415 0.1109 0.1109 0.8415
double double [[{“value”:”{\”value\”:\”0.8415\”}”},{“value”:”{\”value\”:\”0.1109\”}”},{“value”:”{\”value\”:\”0.1109\”}”},{“value”:”{\”value\”:\”0.8415\”}”}]] 2 figure 6f949343-d5b6-4813-8b0a-2c51c881f06b 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 560 420 2 3 4 5 6 7 8 2 4 5 6 7 8 9 10 variable Ni 0 1 1 20 true false x = linspace(-1,1,4) 0 15 15 0 false false f = abs(sin(x.^2)) 1 16 16 1 false false figure 2 18 18 2 false false plot(linspace(-1,1,100),abs(sin(linspace(-1,1,100).^2))); 3 19 19 2 false false hold on 4 20 20 2 false false plot(x,f,’.’,’MarkerSize’,15) 5 21 21 2 false false xlabel(‘x’) 6 22 22 2 false false ylabel(‘f(x)’) 7 23 23 2 false true hold off 8 24 24 2 true false x = 1; 9 38 38 false false i = 2; 10 39 39 false false xpoints = [1,2,3,4,5]; 11 40 40 false false Ni = 1; 12 41 41 false false for l=1:i
Ni = Ni*(x-xpoints(l));
end 13 43 45 false true Ni 14 47 47 3 true false xpoints = linspace(-1,1,4); 15 65 65 false false ypoints = abs(sin(xpoints.^2)); 16 66 66 false false f0 = ypoints; 17 68 68 false false f1 = zeros(1,length(f0)-1); 18 69 69 false false for j=1:length(f0)-1
f1(j) = (f0(j)-f0(j+1))/(xpoints(j)-xpoints(j+1));
end 19 71 73 false true f1 20 75 75 true false xpoints = linspace(-1,1,4); 21 81 81 false false ypoints = abs(sin(xpoints.^2)); 22 82 82 false false f1 = zeros(length(xpoints),length(xpoints)); 23 84 84 false false f1(1,:) = ypoints; 24 85 85 false false for i=1:length(xpoints)-1
for j=1:length(f1)-i
f1(i+1,j) = (f1(i,j)-f1(i,j+1))/(xpoints(j)-xpoints(j+i));
end
end 25 87 93 false false f1 26 94 94 false true disp(f1(end,1)) 27 95 95 true false xpoints = linspace(-1,1,20); 28 100 100 false false ypoints = abs(sin(xpoints.^2)); 29 101 101 false false x = linspace(-1,1,100); 30 103 103 false false f=0; 31 105 105 false false for i = 0:length(xpoints)-1
f = f+divdiff(xpoints(1:i+1),ypoints(1:i+1)).*newton_N(x,i,xpoints);
i
end 32 107 111 false false a = polyfit(xpoints,ypoints,length(xpoints)-1); 33 113 113 false false fit = polyval(a,x); 34 114 114 false false plot(xpoints,ypoints,’.’,’MarkerSize’,15) 35 116 116 false false hold on 36 117 117 false false plot(x,fit,’x-‘) 37 118 118 false false plot(x,f) 38 119 119 false false hold off 39 120 120 false true plot(x,abs(fit-f)) 40 121 121
2020-03-31T14:12:03Z 2020-09-06T02:38:25Z
application/vnd.mathworks.matlab.code MATLAB Code R2020a
9.8.0.1298242 753d191b-d2c5-4eb1-9658-1dcf6a22c437
9.8.0.1417392
R2020a
Update 4
Jun 24 2020
1882048