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Questions tagged [approximation]

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

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1answer
52 views

Is there a function to solve a complicated event probability problem? [on hold]

I need to find the probability of this beast: P[(ABEF)+(CDEH)+(ABEI)+(CDEI)+(ABEJ)+(CDEJ)]. A,B,C, etc. represent events with probabilities close to 0.5 so I don't think rare event approximation can ...
3
votes
3answers
164 views

Approximate the solutions as a series

I would like to solve the following equation $y^2=x^2+ax^2y^2+by^2x^3+cy^3x^2$ where $a,b,c$ are small, so $y\approx x+O(x^3)$. I would like to have a series approximation of the solution rather than ...
1
vote
1answer
36 views

Interpolation error of InterpolatingPolynomial[]

this is my first post so if I have any error while writing this, I'm sorry. I had to do a polynomic interpolation for one of my lab experiments, and I need to get the error from it in order to ...
1
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0answers
28 views

Smoothing the surface created from a set of points

I have a question about "smoothing" the surface created on the basis of a set of points. I would like to get an effect similar to that from the Documentation Center. enter link description here The ...
0
votes
2answers
86 views

Product of large number with a very small number returns zero because Mathematica sets the very small number equal to zero [closed]

I have a product Exp[-I*Pi*x]*BesselK[-1, 2.43*Ix]. Now, Exp[-I*Pi*x] grows larger and larger as $x$ increases for imaginary ...
1
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0answers
134 views

Approximate the relationship between 6 nonlinear functions involving elliptic integrals

I am trying to solve a physics-related problem, which results in approximating a relationship between 6 symbolic functions $F_1(\alpha,\beta ,x_0,y_0),F_2(\alpha,\beta ,x_0,y_0),...,F_6(\alpha,\beta ,...
2
votes
1answer
62 views

How to approximate all values in the formula?

Given E^(t (4.285 - 0.5 Sqrt[1.9994 - 4. wn])) How do I simplify the formula to E^(t (4.2 - 0.5 Sqrt[1.9 - 4. wn]))?
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0answers
38 views

Why exactly is PadeApproximant taking so long here?

*All supporting code is at the bottom of this post, and is understood to precede all other code written here. I have a function $R(E;\{x\})$, where $E$ is the parameter which I am interested in ...
5
votes
1answer
141 views

Numerical solution of KdV equation

I am dealing with the following Cauchy problem for the KdV equation: w'''[t] + 6 w[t] w'[t] - w'[t] = HeavisideTheta[t] w[0] = w'[0] = w''[0] = 0 My problem is ...
1
vote
1answer
60 views

Reciprocal function of a polynomial : Why mathematica doesn't find a solution on my given interval?

I am trying to find a reciprocal function to the binary shannon entropy $H_2(p)$ (chosing the branch were $p>1/2$). I used a method based on solving the differential equation that the reciprocal ...
0
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1answer
148 views

FindRoot fails 100 iteration precision

I am attempting to find roots of a complex equation that involves exponential functions and small approximation values. I have had success using FindRoot for values ...
18
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2answers
248 views

Why this weird return value from `N`?

Bug introduced in 11.3. Why does N just return the exact number below? I want a 2000 digit approximation... ...
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1answer
98 views
0
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0answers
38 views

Obtaining expressions for SDE aprroximation(s)

Appreciate any insight into whether the following is possible and how it might be 'best/properly' done. MMA models quite general Ito Processes, via ItoProcess. ...
0
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1answer
76 views

How to boost the performance of a function that approximates a 3D object

I have defined a function $f_{a}(\boldsymbol{r})$ that gives a finite discrete approximation of a continuous function $f(\boldsymbol{r})$ that represents a 3D object. Here, the object is a sphere of ...
11
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3answers
1k views

François Viète's approximation to π

How do I program the approximation to π devised by François Viète, which is given by 2 * 2/Sqrt[2] * 2/Sqrt[2 + Sqrt[2]] * 2/Sqrt[2 + Sqrt[2 + Sqrt[2]]] * ... ...
0
votes
1answer
173 views

Making a table of solutions from NSolve or Solve

How can I generate a table of solutions to an equation such as this: Solve[{a^m+b==c,b-m==a+Sqrt[n]},{a,b}] for some given values for $n$ and $m$.
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0answers
50 views
1
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0answers
43 views

How can I calculate BezierFunction points by hand? [closed]

For example, I know that the control points are {0, 0}, {1, 0} and {2, 3} and I need to ...
0
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1answer
54 views
0
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0answers
65 views

Error minimization of an approximation scheme

I am trying to check an approximation scheme described in here. So I use NDSolve for both the original equation and Green's function equation. Here is the code I use. ...
1
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1answer
319 views

Encountered non-numerical value for a derivative at t = 0

I am trying to compare an approximation formula for a particular nonlinear ODE with different right hand sides. The code I use is: ...
-1
votes
1answer
50 views

How do I stop mathematica from producing weird numerical errors?

I have here a piece of mathematica code: ...
10
votes
3answers
459 views

Approximation with radial basis functions

I want to approximate some functions with basisfunctions, which can be easy Fourier-transformed. So I got the idea to approximate my function with Gaussian normal-distribution curves. This led me to ...
0
votes
1answer
107 views

Understanding O[]-term logic [closed]

I tried to solve a linear algebraic system with a first order approximation for small parameter "d<<1". Here is a system of linear equations. I found a true solution for it described below ...
0
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1answer
68 views

Find elementary function that fits the data

I have the following data, i.e. a list of points: ...
1
vote
1answer
68 views

How do I find the volume of this box?

I have data points that define the ground and a cubic piece of Styrofoam. the piece of Styrofoam has a cubic hole cut into it. I need to approximate the volume of the hole. I specifically want to do ...
0
votes
1answer
58 views

Plot on a range by using restricted number of points [closed]

Suppose some function. I need to plot it on the given range, but using the finite number of points. After that I need to approximate obtained discrete plot by the curve. Is it possible to do this?
0
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1answer
39 views

The particular approximation of a function

Suppose the function f[x_,y_] := P[x/y]*Sqrt[1-x^2/y^2] + F[x/y]*Log[(1-Sqrt[1-x^2/y^2])/(1+Sqrt[1-x^2/y^2])] Here $P[x,y], F[x,y]$ are polynomial of some ...
2
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3answers
185 views

Finding a polynomial representation for a sum function

I'm trying to find a polynomial representation for this horrendous function: $$f(x)=\frac{\frac{1}{2}-\frac{4}{1+10,000x}\sum_{n=0}^{\infty}\frac{(-1)^n}{\big[\big(n+\frac{1}{2}\big)\pi\big]^4}\tanh\...
1
vote
2answers
75 views

How to approximate only number but not the numeric indices in an equation? [duplicate]

I need to solve a system of equations. It would be too long to solve it exactly, so I need to approximate by numbers the coefficients. The problem is the following : ...
1
vote
2answers
102 views

Finding Asymptotics for a Series

How can I find a simple expression that's asymptotic to $\sum_{i=1}^{n-1}2^i/i$? That is, Sum[2^i/i,{i,1,n-1}]. According to https://reference.wolfram.com/...
17
votes
2answers
700 views

Series sum approximation

Since there is no closed formula, as far as I know, to find the sum of $$ \sum _{n=2}^{\infty } \frac{(-1)^n}{\sqrt{\log (n)}} $$ I used //N to find an ...
2
votes
3answers
325 views

Obtaining minimax polynomial from an interpolation function

I have an interpolation function f: ...
3
votes
1answer
74 views

Quick, dirty, imprecise way to find the root of a definite integral?

I'm trying to find a value x that satisfies an equation of the form $y=\int_0^xf(x')dx'$. As far as I can tell, there's no closed-form solution for $y$, or $dy/dx$, so when I plug this into Solve, ...
1
vote
1answer
88 views

I'd like to make an approximate approximation [closed]

This is my code: ...
1
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4answers
216 views

Finding 25 points nearest to an approximation line

I have to find 25 points that lie nearest to a linear approximation of my data. This is my source code: ...
2
votes
2answers
74 views

Extract from sum only terms with exponents satisfying a specific condition

Consider an equation eq = x1^n x2^m s^a+ c+ x1^g s^r x2^l+..so on n, m, a, g, r and l are known real numbers and equation contain lots of these terms. I want to ...
0
votes
0answers
99 views

approximations and limits

My question is related to this one: Approximating for $a \gg b$ I have a rather complex symbolic expression of interest. The expression is comprised of about ten different symbolic quantities. I wish ...
0
votes
1answer
49 views

Series expansion in terms of functions and derivatives

I have an expression involving two functions and their derivatives to some powers. I want to obtain a linear expression in functions and their derivatives. How can I do that in Mathematica?
26
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4answers
1k views

How can I adaptively simplify a curved shape?

For the purposes of creating a publication-quality plot marker I wish to convert a font glyph into a simplified Polygon where points are taken adaptively according ...
5
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5answers
332 views

Continued fraction approximation for $\pi$

How to code this formula in Mathematica to approximate $\pi$? Thanks for your help! $$\frac4{\pi}=1+\cfrac{1^2}{2+\cfrac{3^2}{2+\cfrac{5^2}{2+\cfrac{7^2}{2+\cdots}}}}$$
4
votes
1answer
102 views

How to Approximate at Non-differentiable Point (forced Series Expansion around Branch Cut)

I need a numerical approximation around some functions at $x = 0^{-}$ from the left side, where $x = 0$ is unfortunately the right end of the domain (in the reals) so the functions are not ...
3
votes
1answer
70 views

Approach a function given some points and its maximum

For example, I know that a function goes through the points (2.01, 96), (4, 160), (8.1, 257) and (13.1, 321), and that its maximum is 397. Is it possible to approach the function with this data?
3
votes
1answer
140 views

Integral approximation using a matrix operator

In the paper "Chebyshev solution of differential, integral and integro-differential equations" (it is freely accessible and can be downloaded from the link), El-gendi uses a method to approximate the ...
0
votes
1answer
73 views

How to include zeros at the end of an approximation [closed]

I want to make a table for my calculus 1 class learning limits. I am calculating $\lim_{x\to 0} \frac{sin(x)}{x}$. I am using the approximation given by N. The problem is with the expression up to 15 (...
7
votes
2answers
307 views

Finding out the closest approximation of a decimal number by a ratio of two integers

Given a decimal number, which is positive but can be less than or greater than one, how to find out its best approximation by a ratio of two integers in a given range? For example, given a number <...
7
votes
2answers
224 views

Can I get Mathematica to recognize common series expansions of trigonometric functions?

I have some complicated functions from numerical procedures that go to simple trig functions in the limit of small time-steps. For example, I can calculate that one of these functions goes to: ...
2
votes
3answers
193 views

How to approximate this bell-shaped integral function using Mathematica?

Consider the following function : $$\tag{1} f(v) = v^{\frac{d}{2}} \int_v^{\infty} u^{a \,-\, \smash{\frac{d}{2}} \,-\, 1} \; e^{-\, a \, u} \; du, $$ where $a$ and $d$ are two positive constants (...
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vote
2answers
49 views

Using N more than once in a computation [closed]

So I'm trying to enter a function that computes Pi to the nth place divided by Pi to the mth place, so to do that I started with actual numerical values. I tried ...