# Tagged Questions

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312 views

### Find parameters that minimize the distance between two curves in terms of the infinite norm

I am trying to implement a very simple NMinimize code that would search for parameters of a polynomial that minimize (globally) the distance between this polynomial ...
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### Finding input of the function $f(a,b,c) = (d,e)$ such that $|d-e|$ = constant for $d\in[d_0,d_1]$

The actual question contains a few more parameters than mentioned in the title, but the idea will remain very similar. Lets begin abstractly; I have a certain function $f(a,b,c) = (d,e,g,h)$. I am ...
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### Approximate analytic solution to a polynomial equation

The analytic solution of the equation $$1-\frac{2M}{r}+\frac{Q^2}{r^2}-\frac{\Lambda}{3}r^2 = 0$$ obtained by using the code ...
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### Why does MiniMaxApproximation fail in this simple case?

Why does MiniMaxApproximation[Erfc[t], {t, {0, 2}, 0, 1}] give the following error? ...
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### Looking for a convenient way to replace a large data sample with an analytic approximation

Suppose that data is a large data sample, and that Histogram[data] produces a very smooth-looking distribution. Since ...
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### Chebyshev Approximation

Is there functionality in Mathematica to expand a function into a series with Chebyshev polynomials? The Series function only approximates with Taylor series.
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### Use NMinimize instead of FindFit for constrained search (of coefficients)

(My problem is more complex, but let us formulate it through this example) I am trying to find the best polynomial approximation to the following function ...
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### 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 ...
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### How to derive finite-difference scheme automatically on a quite general stencil

Info This question is a generalization of the following one Derivation of numerical scheme for linear transport equation on a variable stencil. Statement of a problem Linear scalar hyperbolic (...
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### How does WolframAlpha calculate closed form approximations of irrational numbers? [closed]

How does WolframAlpha do this: I'm aware of services such as RIES, which is an inverse equation solver, and ISC, the Inverse Symbolic Calculator. But WA goes much further. I've tried doing a ...
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### Trying to find the best Padé approximant for a given number of terms

Let suppose that I have a function $f[x]$ I want to approximate using a Padé expansion and that I decide what would be maximum number of terms to be used. Is there any way with Mathematica to find ...
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### 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. ...
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### 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 ...
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### 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 ...
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### The 1st approximation of multi-viables which contains the differential [closed]

When I input to Mathematica as following, ...
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### I want to cut off secondary approximate parts

When I input to Mathematica as follows, ...
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### Showing separate surfaces

The XYZPipeJunction is removed using circular trig functions from Both. ...
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### 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<= ...
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### 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? $f(t)=\int_0^{\infty}\frac{K_1a(t)}{a(t)+K_2}\,dt$ ...
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### 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... ...
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### 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 ...