Calculate f(4) using newton's interpolating polynomials of order 1 through 4. Choose your base points to attain good accuracy.

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Quinten 2016-11-1

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回答： Tamir Suliman 2016-12-14

x = [1 2 3 5 7 8];
y = [3 6 19 99 291 444];

I know I need a polval function like

xx = 1:8;
yy = polyval(xx,n);

I just don't know where to go from there.

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Jan 2016-11-2

@Quinten: We cannot guess, what f() is. Without knowing this detail, the question is not meaningful.

Walter Roberson 2016-11-2

Is the assignment to do with being passed in a function handle, and you are to apply the interpolation for the passed function handle evaluated at parameter 4?

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Tamir Suliman 2016-12-14

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https://ww2.mathworks.cn/matlabcentral/answers/310196-calculate-f-4-using-newton-s-interpolating-polynomials-of-order-1-through-4-choose-your-base-point#answer_247110

在 MATLAB Online 中打开

Check this code though I m not sure

function newton_interpolation(x,y,n,xx)
% x and y are two Row Matrices 
% and xx is point of interpolation
% n is the order number which should be less than the matrix size
a(1) = y(1);
for k = 1 : n - 1
   d(k, 1) = (y(k+1) - y(k))/(x(k+1) - x(k));
end
for j = 2 : n - 1
   for k = 1 : n - j
      d(k, j) = (d(k+1, j - 1) - d(k, j - 1))/(x(k+j) - x(k));
   end
end
d
for j = 2 : n
   a(j) = d(1, j-1);
end
Df(1) = 1;
c(1) = a(1);
for j = 2 : n
   Df(j)=(xx - x(j-1)) .* Df(j-1);
   c(j) = a(j) .* Df(j);
end
fp=sum(c)
plot(x,y)
      title('Newton  Interpolation ')
      xlabel('x - value')
      ylabel('y - value')
      axis([min(x)-1 max(x)+1 0 max(y)+50])
      grid on