How to generate interpolating polynomial using Newton formula for exponential function?
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I am trying to find interpolating polynomial of $f(x) = e^{3x}$ and interpolation nodes $x_0=x_1=x_2 = 0 and x_3 = x_4 = 1 $ with Newton's formula using Wolfram Alpha, but I am stuck with division of zero trying to find divided differences like so:
Do[Do[roots[i,j] = (roots[i - 1, j + 1] - roots[i - 1, j]) / (nodes[i + j] - nodes[j]), {j, 0, n - i}], {i, 1, n}];
Can you guys tell me what I do wrong? Perhaps my formula is wrong or I am misunderstanding something, I gotta admit I am new to Numerical Analysis and Wolfram Mathematica.
interpolation wolfram-alpha
asked Dec 18 '18 at 20:00
kuskmenkuskmen
1014
$endgroup$
add a comment |
$begingroup$
I am trying to find interpolating polynomial of $f(x) = e^{3x}$ and interpolation nodes $x_0=x_1=x_2 = 0 and x_3 = x_4 = 1 $ with Newton's formula using Wolfram Alpha, but I am stuck with division of zero trying to find divided differences like so:
Do[Do[roots[i,j] = (roots[i - 1, j + 1] - roots[i - 1, j]) / (nodes[i + j] - nodes[j]), {j, 0, n - i}], {i, 1, n}];
Can you guys tell me what I do wrong? Perhaps my formula is wrong or I am misunderstanding something, I gotta admit I am new to Numerical Analysis and Wolfram Mathematica.
interpolation wolfram-alpha
asked Dec 18 '18 at 20:00
kuskmenkuskmen
1014
$endgroup$
add a comment |
$begingroup$
I am trying to find interpolating polynomial of $f(x) = e^{3x}$ and interpolation nodes $x_0=x_1=x_2 = 0 and x_3 = x_4 = 1 $ with Newton's formula using Wolfram Alpha, but I am stuck with division of zero trying to find divided differences like so:
Do[Do[roots[i,j] = (roots[i - 1, j + 1] - roots[i - 1, j]) / (nodes[i + j] - nodes[j]), {j, 0, n - i}], {i, 1, n}];
Can you guys tell me what I do wrong? Perhaps my formula is wrong or I am misunderstanding something, I gotta admit I am new to Numerical Analysis and Wolfram Mathematica.
interpolation wolfram-alpha
asked Dec 18 '18 at 20:00
kuskmenkuskmen
1014
$endgroup$
I am trying to find interpolating polynomial of $f(x) = e^{3x}$ and interpolation nodes $x_0=x_1=x_2 = 0 and x_3 = x_4 = 1 $ with Newton's formula using Wolfram Alpha, but I am stuck with division of zero trying to find divided differences like so:
Do[Do[roots[i,j] = (roots[i - 1, j + 1] - roots[i - 1, j]) / (nodes[i + j] - nodes[j]), {j, 0, n - i}], {i, 1, n}];
Can you guys tell me what I do wrong? Perhaps my formula is wrong or I am misunderstanding something, I gotta admit I am new to Numerical Analysis and Wolfram Mathematica.
interpolation wolfram-alpha
interpolation wolfram-alpha
asked Dec 18 '18 at 20:00
kuskmenkuskmen
1014
asked Dec 18 '18 at 20:00
kuskmenkuskmen
1014
asked Dec 18 '18 at 20:00
kuskmenkuskmen
1014
asked Dec 18 '18 at 20:00
kuskmenkuskmen
1014
asked Dec 18 '18 at 20:00
kuskmenkuskmen
1014
1014
add a comment |
add a comment |
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