Questions tagged [approximation]
Questions on approximating functions (e.g. PadeApproximant), approximating integrals, working with approximate values (e.g. RootApproximant) etc.
215 questions
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Approximately solving this equation among probabilities/LLRs symbolically
Consider three independent Bernoulli events $A, B, C$ with success probabilities $p, q$ and $r$ respectively. Let us define two more derived events $L$ and $M$ with probabilities $p_1$ and $p_2$ given ...
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Approximating Bessel $K_0$
I often face a problem that some special functions are not readily available in common programming languages (e.g. Fortran) without using specialised libraries. Therefore I want to be able to quickly ...
- 25k
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How do we find an asymptotic approximation of the function $\mathbf{P}(r)=\left(t_1+\prod\limits_{k=1}^{r}(t_2+k^{s})\right)^n$?
Suppose we have the following function, where $s\in\mathbb{R}$ and $t_1,t_2,n\in\mathbb{N}\cup\{0\}$ are constants:
$$\mathbf{P}(r)=\left(t_1+\prod_{k=1}^{r}(t_2+k^{s})\right)^n$$
Question: What is ...
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How to find "minimal polynomial" of a rational number?
I suspect that 1.0982 is (close to) the root of a low degree (2 or 4) polynomial with small ...
- 1,466
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How to approximate an implicit function using simple functions (e.g. polynomials)?
I am trying to approximate the following function using taylor series (to express $y$ as an explicit function of $x$ for $0.3<y<1$):
$$
x = a (1-y)^b + c \sinh(d (1-y))
$$
where $a$, $b$, $c$, ...
- 641
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Why do two equivalent expressions yield different numerical results when using differentiation matrices?
I am computing an expression numerically in two different ways and obtaining a non-zero result when taking the difference between the two. Can you please help me understand the discrepancy?
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How to get series expansion of this expression involving Gamma function?
I have the following code
...
- 641
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Double sum error message for NSum
I am attempting to evaluate
NSum[1/((2 i + 1)^4 + (2 j + 1)^4), {i, -1000, 1000}, {j, -1000, 1000}]
but it gives a negative value as the result; alongside an error ...
- 797
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Solving a complicated equation for approximate analytical solution
I am trying to solve the Following equation for r,
2*a*Q^4 + 5*r^4*(-4*Q^2 - 2*r*(-3*M + r) + 3*c*r^(1 - 3*\[Omega])*(1 + \[Omega])) ==0
Clearly this is unsolvable....
- 159
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Calculating relative error of Ramanujan formula for ellipse perimeter
On this page, they present the Ramajujan's second formula for the perimeter of an ellipse:
$$P \approx \pi (a+b) \left(1+ \frac{3 h}{\sqrt{4-3 h}+10}\right),$$
where $h=(a-b)^2/(a+b)^2$. They expand ...
- 199
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Is there a way in Mathematica to simplify expressions based on inexact assumptions? [closed]
Is there a way in Mathematica to simplify expressions based on inexact or "relative" assumptions such as $x<<y$ or $x\approx y$?
I see ...
- 3,790
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How to get an easy to compute representation defined by plot of involved function?
I am doing a windmill vortex sheet calculation where I have to guess its shape and then vorticity distribution and then make sure that the net flow is along the sheet. The problem is adjusting my ...
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How can I approximate a function with composite polynomials?
I know that to approximate a function with for example $f(x) = \sin(x)$ using polynomials with degrees up to 4, I can use the Fit function :
...
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How can I get samples of f(x) that are roughly evenly spaced?
I am looking for an efficient way of getting 60 to 80 samples of an arbitrary f(x) such that the distance between adjacent samples are approximately equal. My first attempt is based on a first order ...
- 7,194
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How can we obtain an approximate simplified equation (QsNr) from a set of given equations using Mathematica?
I am trying to find an approximate equation for a complicated expression (QsNr) using Mathematica. The equation involves several parameters and expressions, and I want to simplify it by considering ...
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