Mixing
Lagrange Polynomials with Derivatives (lowest order polynomial)
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I need to find the lowest order polynomial, $P(x)$, that satisfies the following conditions using Lagrange polynomials:
$P^{'}(x_{0}) = f_{0}^{'}$
$P^{'}(x_{1}) = f_{1}^{'}$
$P^{'}(x_{2}) = f_{2}^{'}$
$P^{'}(x_{3}) = f_{3}^{'}$
with $x_i neq x_j$ when $i neq j$
I understand how to find the Lagrange polynomials, but I am not sure how to satisfy the derivative conditions. Is a quadratic or cubic interpolation needed? Thank you.
polynomials interpolation lagrange-interpolation
asked Jan 24 at 20:25
robertrobert
165
$endgroup$
add a comment |
$begingroup$
I need to find the lowest order polynomial, $P(x)$, that satisfies the following conditions using Lagrange polynomials:
$P^{'}(x_{0}) = f_{0}^{'}$
$P^{'}(x_{1}) = f_{1}^{'}$
$P^{'}(x_{2}) = f_{2}^{'}$
$P^{'}(x_{3}) = f_{3}^{'}$
with $x_i neq x_j$ when $i neq j$
I understand how to find the Lagrange polynomials, but I am not sure how to satisfy the derivative conditions. Is a quadratic or cubic interpolation needed? Thank you.
polynomials interpolation lagrange-interpolation
asked Jan 24 at 20:25
robertrobert
165
$endgroup$
2
$begingroup$
Since all conditions are for first derivatives, you can just interpolate $P'$ and integrate it to get $P$.
$endgroup$
– Ian
Jan 24 at 20:30
add a comment |
$begingroup$
I need to find the lowest order polynomial, $P(x)$, that satisfies the following conditions using Lagrange polynomials:
$P^{'}(x_{0}) = f_{0}^{'}$
$P^{'}(x_{1}) = f_{1}^{'}$
$P^{'}(x_{2}) = f_{2}^{'}$
$P^{'}(x_{3}) = f_{3}^{'}$
with $x_i neq x_j$ when $i neq j$
I understand how to find the Lagrange polynomials, but I am not sure how to satisfy the derivative conditions. Is a quadratic or cubic interpolation needed? Thank you.
polynomials interpolation lagrange-interpolation
asked Jan 24 at 20:25
robertrobert
165
$endgroup$
I need to find the lowest order polynomial, $P(x)$, that satisfies the following conditions using Lagrange polynomials:
$P^{'}(x_{0}) = f_{0}^{'}$
$P^{'}(x_{1}) = f_{1}^{'}$
$P^{'}(x_{2}) = f_{2}^{'}$
$P^{'}(x_{3}) = f_{3}^{'}$
with $x_i neq x_j$ when $i neq j$
I understand how to find the Lagrange polynomials, but I am not sure how to satisfy the derivative conditions. Is a quadratic or cubic interpolation needed? Thank you.
polynomials interpolation lagrange-interpolation
polynomials interpolation lagrange-interpolation
asked Jan 24 at 20:25
robertrobert
165
asked Jan 24 at 20:25
robertrobert
165
asked Jan 24 at 20:25
robertrobert
165
asked Jan 24 at 20:25
robertrobert
165
asked Jan 24 at 20:25
robertrobert
165
165
2
$begingroup$
Since all conditions are for first derivatives, you can just interpolate $P'$ and integrate it to get $P$.
$endgroup$
– Ian
Jan 24 at 20:30
add a comment |
2
$begingroup$
Since all conditions are for first derivatives, you can just interpolate $P'$ and integrate it to get $P$.
$endgroup$
– Ian
Jan 24 at 20:30
2
2
$begingroup$
Since all conditions are for first derivatives, you can just interpolate $P'$ and integrate it to get $P$.
$endgroup$
– Ian
Jan 24 at 20:30
$begingroup$
Since all conditions are for first derivatives, you can just interpolate $P'$ and integrate it to get $P$.
$endgroup$
– Ian
Jan 24 at 20:30
add a comment |
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$begingroup$
Since all conditions are for first derivatives, you can just interpolate $P'$ and integrate it to get $P$.
$endgroup$
– Ian
Jan 24 at 20:30