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16
votes
1answer
250 views

How can I smooth a 3D surface generated by RegionBoundary?

I have a set of points that belong to the surface of an object. I would like to approximate a surface to which I can compute the distance. of other points. With the nice code of this post, I was able ...
0
votes
0answers
80 views

How to make a twice-differentiable function that approximates some data?

I have some time series data that I would like to approximate with a twice-differentiable function. Each time series has ~10,000 datapoints, so I definitely do not want a function that passes through ...
2
votes
0answers
43 views

Computing an inexact derivative with some terms preserved in exact form

I am beginning to learn Mathematica and have the following question: How can I return a derivative with exact numbers instead of one involving numerical approximations? My original, single variable ...
1
vote
1answer
121 views

Approaches to solving non-linear systems of equation with assumptions

The specific type of system looks as follows: \begin{align} (r-r')x+4d_1 x^3+4d_{12}xy^2 &= 0 \\ (r+r')y+4d_2 y^3+4d_{12}yx^2 &= 0 \\ \end{align} Where $r,r',d_1, d_2, d_{12}$ are all real ...
2
votes
2answers
253 views

Perturbation theory with Mathematica: Definite integral of polynomial times exponential times hypergeometric function of imaginary argument

I would like to ask also Mathematica users about my question from the math forum. To expand, I'm adding the code which calculates the full double integral for $n=0$ and $\mu=0$ (the second in the ...
5
votes
5answers
143 views

Isolating cross terms

I have a set of expressions that contains terms like $\frac{1}{(x + a + b)(c+d)}$. I would like to simplify the denominator so that products of $a,b,c,d$ are dropped, but $x c$ and $x d$ are kept. ...
3
votes
1answer
184 views

Series approximation to integral

I would like to approximate the integral $$ \int_0^\infty dy\,\frac{1}{\sqrt{2\pi y\sigma^2}}\exp\left(-\frac{(x-y)^2}{2y\sigma^2}\right)f(y), $$ as a series expansion in the limit $\sigma\rightarrow ...
2
votes
2answers
84 views

Approximation of $f(x)$ at large values of $x$?

Suppose you a function $f(x)=1/x+x^2$. At large values of $x$, it is closely approximated by $f(x)=x^2$. Can Mathematica do this for me for a more complicated function? How would I input the ...
6
votes
2answers
191 views

Efficient Lloyd Sampling of Images

I want to sample a grayscale image so that every voronoi cell contains approximately the same total intensity using lloyd sampling. My current code is kind of slow and I was hoping for some advice to ...
0
votes
0answers
68 views

Applying the square root of operator on polynomial functions

I am trying to apply an "operation" on polynomial functions: apply the operator $(\frac{\partial f}{\partial x}-y\frac{\partial f}{\partial z})^2+(\frac{\partial f}{\partial y}+x\frac{\partial ...
0
votes
1answer
74 views

The 1st approximation of multi-viables which contains the differential [closed]

When I input to Mathematica as following, ...
0
votes
4answers
105 views

I want to cut off secondary approximate parts

When I input to Mathematica as follows, ...
1
vote
1answer
243 views

Showing separate surfaces

The XYZPipeJunction is removed using circular trig functions from Both. ...
2
votes
1answer
158 views

Seeking simple function in interval

I am a bit rusty, and struggling to solve this problem. Looking for a simple, well behaved parametric function f[t], from [0,1] to [0,1] such that: f[0] = f0; f[1] = f1; f'[1] = ff1; where -1<= ...
0
votes
1answer
91 views

How to obtain Padé approximant of $\log(x)$? [closed]

Having read this answer on Math.SE, I wanted to try seeing how Padé approximations converge to $\log(x)$. But my first attempt after reading the documentation failed: ...
0
votes
1answer
55 views

Integral evalutation

I am trying to integrate the following expression over $L$. E^(-2 L n) (1 - L/(2 s))^(-1 + 4 n µ) (L/s)^(-1 + 4 n v) I did... ...
4
votes
2answers
276 views

Approximation to the prime counting function

Is there a function similar to PrimePi that gives approximate value for large numbers? In particular, I need a reasonably good approximation for $\pi(x)$, where ...
7
votes
4answers
622 views

Solving $L=\frac{3}{2} \sqrt{4 \pi ^2 A^2+W^2}-\frac{\sqrt{5 W \sqrt{4 \pi ^2 A^2+W^2}+6 \pi ^2 A^2+3 W^2}}{\sqrt{2}}+\frac{3 W}{2}$ for $W$

When I solve the aforementioned equation for $W$ or $A$ on Mathematica I get a long and ugly equation in return, namely one of the solutions for $W$ is: (attempt to read at your own health) ...
2
votes
1answer
119 views

How to generate specific function using BSpline command/

I want to generate an approximation function that fits a curve to points. My goal is to obtain an actual formula. Is this possible with the BSpline function? Using the following code: ...
0
votes
0answers
109 views

How do I estimate the Pareto front in my multiobjective optimization problem?

I need to minimize a function of two parameters that gives two "stress" outputs {A,B} = f[tau,mu]. How do I estimate (even roughly), the Pareto front for this ...
0
votes
3answers
337 views

Solving an Integral Numerically

I have been trying to solve the integral equation below, but cant seem to find a way out of this. Can someone please help me out with suggestion? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
1
vote
1answer
165 views

Trying to find the best Pade approximant for a given numer of terms

Let suppose that I have a function $f[x]$ I want to approximate using a Pade expansion and that I decide what would be maximum number of terms to be used. Is there any way with Mathematica to find ...
1
vote
2answers
238 views

How can I get an approximate contour plot from a 3D plot?

I have some larger square, Hermitian matrices, M, (dimension 20, say, much more than 4) with 2 independent variables, call them x and y. I can plot the eigenvalues as functions of x and y with: ...
3
votes
2answers
355 views

Assigning an analytical approximation to the error function erf(x)

Working with some iterative integral equations, I have Gaussian density functions involved therein. Integrating the Gaussian function I obtain the error function. When I take the second integration, ...
1
vote
0answers
163 views

Compute coefficient of Generating function

Given a generating function $F(z)$, is there any way to compute the coefficient $a_k$ of $z^k$ by Mathematica? One method is to calculate by the equation $\frac{F^{(k)}(0)}{k!}$. However, this ...
11
votes
2answers
797 views

How to improve the accuracy of this Monte Carlo simulation

A friend of mine went on an interview and he was asked to calculate the angle between the hour hand and minute hand of an analog clock when the time was 3:15. Arguably, this is a trivial problem that ...
1
vote
2answers
333 views

Approximate solution to system of polynomial equations

I'd like to solve approximately the following system of equations for $a_1$, $a_2$, $\alpha_1$ and $\alpha_2$ all real and nonzero: ...
0
votes
2answers
511 views

How to visualise an iterative approximation to pi

I'm experimenting with different algorithms that approximate pi via iteration and comparing the result to pi. I want to both visualise and perhaps know the function (if any) that describes the ...
1
vote
0answers
66 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
votes
2answers
224 views

Formatting results of integral approximation methods comparison.

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
159 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
127 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. ...
1
vote
1answer
381 views

Relative error plot [duplicate]

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 ...
0
votes
1answer
505 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
vote
2answers
355 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 ...
5
votes
1answer
460 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
324 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
397 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 ...
5
votes
1answer
1k 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) = ...