The approximation tag has no wiki summary.
1
vote
0answers
42 views
Decimal representations of analytic values in an expansion
I have a solution to an ODE (which I call sol), which I would like to expand in terms of Log[1+x] around x=-1. I thought that:
...
0
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2answers
71 views
Need help creating a `Table` that shows midpoint, trapezoidal and Simpson's rule approximations of an integral with 4 different subintervals
The integral is Integrate[Sqrt[1+x^3], {x, -1, 1}]. I want to create a Table with three columns and four rows that shows the ...
3
votes
1answer
57 views
Find root approximants for low-precision numbers
I want to be able to find low-complexity algebraic approximants to decimal numbers. For example, 1.41 can be approximated as a solution to the polynomial x^2==2. ...
2
votes
0answers
88 views
Smooth Max and Abs
I'm trying to implement smooth approximations of Max and Abs functions. Moreover I want the functions to map element-wise on tensors. Here's my code.
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1
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1answer
135 views
Relative error plot
I was plotting the relative error of the $e^{11/12 -n}n^{n+1/2}$ approximation to $n!$ as $n$ gets larger and larger, and at some very large value of $n$ Mathematica gives this plot:
Can somebody ...
-1
votes
1answer
170 views
Multivariate Function Approximation With a Large Dataset
I have a nice amount of data from a trading strategy I am working on, where I have two different liquidity parameters as x, y variables.
Before entering a trade I am taking the moving average of ...
1
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2answers
152 views
Calculating error of the approximate formula in calculations
I have an exact equation:
\begin{equation}
a = \sqrt{1 + x^2 - \sqrt{(1 + x^2)^2 - 2 x^2 \cos^2\theta}}\tag{1}
\end{equation}
and its approximation:
\begin{equation}
a = \dfrac{x ...
4
votes
1answer
231 views
Time approximation of decrypting RSA algorithm
I've written a function that encrypts a text using the RSA algorithm. It then decrypts it using prime factorization, and takes the time it took to decrypt it and puts it in a vector together with the ...
6
votes
1answer
160 views
GeneralMiniMaxApproximation - Dividing out the zero
MiniMaxApproximation is used to generate minimax approximations. I'm interested in the "dividing out the zero" trick.
The documentation discusses a nice example. Suppose we want to construct a ...
3
votes
1answer
157 views
Small Issue with Chebyshev Derivative Appoximation
I am trying to get approximate the derivative of a function from its Chebyshev expansion.
I start out with the following random function
...
4
votes
1answer
324 views
Polynomial Approximation from Chebyshev coefficients
I would like to expand a function $f(r)$ in the domain $[0,R]$, around the points $r =0$, and $r = R$ in the following manner
$f(r = 0) = \Sigma_{i=0,i = even}^{imax} f_i (r/R)^i$
and
$f(r = R) = ...
