A Padé approximation is the use of a ratio of polynomials to approximate a function. This can be seen as a generalization of the Taylor series which can better account for singularities in the function.
Questions tagged [pade-approximation]
59 questions
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How is this method of fitting a Padé approximant to data called?
This website shows an implementation in R that fits a Padé approximant:
$$
R(x)= \frac{\sum_{j=0}^m a_j x^j}{1+\sum_{k=1}^n b_k x^k}=\frac{a_0+a_1x+a_2x^2+\cdots+a_mx^m}{1+b_1 x+b_2x^2+\cdots+b_nx^n}
$$
to some data.
They write the function like…
Gimelist
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Pade approximation of $\frac{1-e^{-x}I_0(x)}{x}$
I need to expand $\frac{1-e^{-x}I_0(x)}{x}$ in Pade approximation. The answer should be $\frac{1}{1+x}$. But I'm not sure how to reach the answer.
Here $I_0(x)$ is modified Bessel function of order 0 and is given by $$I_0(x)=\sum_{s=0}^\infty…
Septacle
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Pade Approximation Calculate Coefficients when encountering Singular Matrix?
I will be using this post here as a reference:
How to compute the pade approximation?
After getting to the point where you solve a system of linear equations:
$$p_0 = a_0q_0\\p_1 = a_1q_0+a_0q_1\\ \ldots \\p_m = a_mq_0+a_{m-1}q_1+ \,\ldots…
D A
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How to calculate two-point Padé approximant?
Wikipedia mentions two-point Padé approximant. I don't have access to the reference provided (Yoshiki Ueoka, Introduction to multipoints summation...).
I checked also chapter 8 (The N-Point Padé Approximants) in the George A. Baker's Esssentials of…
hans
- 151
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1 answer
why are there two different Pade approximation of delay
There are 2 different second order pade approximations of delay given in internet
What is the difference between these two approximation? Which one is the correct Pade approximation
ShiS
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Pade Approximation of $\sin(x)$
So I am trying to get a polynomial approximation for $\sin(x)$ using Pade approximation for $n = 2$ and $m = 3$ and the Maclaurin series $(\deg 5)$ for
$$\sin(x) = x - \frac{x^3}{3!} + \frac{x^5}{5!}$$
However, the matrix I am getting seems to be…
xCanaan
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close form denominator pade approximation
How it is possible to get the denominator pade close form of the function
$$\frac{1}{2} \left(\sqrt{2 \pi } e^{x/2} \sqrt{x} \text{erf}\left(\frac{\sqrt{x}}{\sqrt{2}}\right)+2\right)$$
as
$$2^{-n-1} \binom{4 n}{2 n} \, _1F_1\left(-n;\frac{1}{2}-2…
user167276
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How are these equations derived?
In the below snippet, the equations are listed that need to be used to solve for the Padé approximant. How are these equations derived? I get they want the derivatives to be equal at zero, but I don't see how those equations follow from that…
saei
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Pade Approximant on Mathematica
I would like to know how to code Pade Approximation on Mathematica.
And also I have solved Eigen values and have 20 coefficient values,but I am not sure how to code on mathematica.Can you please explain me how to code and get values using Pade…
XXXXX
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Is it possible to find the Padé approximation for $\ln{(1+x)}$?
On the Padé approximant wiki, people present various form of padre approximant for $\sin{(x)}, \exp{(x)}$, erf$(x)$ but does not provide instruction on how to create them.
What would be the correct way to find the Padé approximant for $\ln{(1+x)}$…
