# Questions tagged [approximation]

Questions on approximating functions (e.g. PadeApproximant), approximating integrals, working with approximate values (e.g. RootApproximant) etc.

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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 ...
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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....
436 views

### 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 ...
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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 ...
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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 ...
• 7,154
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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 ...
1 vote
118 views

### How to invert this function when the argument e is small?

I need to find an analytical solution the following equation for e in terms of n and p ...
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1 vote
57 views

### Graph lines do not show dashes [closed]

I have the following code of an iteration: ...
40 views

### How to treat small numbers in order to gain efficiency and precision in neural network algorithm?

Unfortunately I won't be able to provide a MWE, as it would be too big and complex, and this question will be based on pure semantics, basically (and I understand if this is impossible to answer in ...
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### How to ask Mathematica to give me possible closed forms from a given numerical approximation

Imagine I am solving a some Infinite Series and I cannot directly compute the value using Mathematica. The value of this series approximates $0.785398....$ (Actually is $\frac{\pi}{4}$). I want to be ...
90 views

### Calculation of Approximate Equation with Mathematica

I am trying to find an approximate equation for a complicated expression (L1, L2) using Mathematica. The equation involves several parameters and expressions, and I want to simplify it by considering ...
1 vote
126 views

### How to obtain approximate form for a calculation using Mathematica with specific approximations?

I am currently working on a calculation in Mathematica that involves various parameters, including Nb, k, and Ns. I want to obtain an approximate form of the calculation by considering the following ...
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### Approximate an expression with condition

I do the following computation: ...
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### How to find an approximate equation from a given equation using Mathematica? [closed]

I am interested in finding an approximate equation based on a given equation using Mathematica. Specifically, I am working with the quantum illumination transmitter's quantum Chernoff bound (...
441 views

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### Using FindFit for Approximation Fourier Series

I am expecting to have a list of discrete points, which I would like to approximate using Fourier's series, then plot Fourier series approximation alongside with discrete points, then plot terms of ...
1 vote
159 views

### Wolfram Mathematica Monte Carlo for integrals approximation

I wanted to implement the Monte Carlo method for multiple integrals approximation in Wolfram Mathematica. Namely I wanted to let the user insert as input the dimension of the integral and the number ...
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154 views

### How can I calculate complicated infinite sums with FindIntegerNullVector (or related methods)?

I've recently been very interested in the wonderfully complex world of Euler sums, i.e. (convergent) infinite sums that, roughly speaking, consist of some rational polynomial combination of ...
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### Can we approximate a matrix power series like NSum does?

Essentially, the following does not work, and I'm wondering if it can be made to: NSum[ MatrixPower[B,n], {n,0,∞}] (Here B is a ...
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1 vote
142 views

### Analytic continuation of a data set from the upper complex plane to the lower complex plane?

Context I am interested in identifying damped modes such as those in self gravitating galaxies: This requires extending to the lower complex plane a dispersion relation which is computed numerically ...
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1 vote
487 views

### Finding a closed-form solution or a better approximation to a function in Mathematica

I have the following equation: $$f(L) = \left\lfloor{\frac{1}{4}\sum_{n=1}^{L-1}\left\lfloor n+300\times2^{n/7}\right\rfloor}\right\rfloor$$ where $1\leq L \leq 99$ My goal is to find a closed-form ...
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