# Tagged Questions

This tag concerns computational problems central to mathematical and scientific computating. The scope includes algorithms, numerical analysis, optimization, and linear algebra, computational topology, computational geometry, symbolic methods, and inverse problems.

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### Minimization Optimization

MAPE (Mean Average Percentage Error):Let $\left\{p_{1},p_{2},p_{3},p_{4}\right\}$ be the numbers $1,-4,4,-5$ respectively. Find the number $x$ that minimizes the Mean Average Percentage Error, \...
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### System of ODEs Matrix Representation?!

Task: Consider the system of first-order ODES: \begin{align*} y_1' =&5y_2-y_1+y_3\\ y_2'=&3y_1-y_2+t^2\\ y_3'=&y_3-ty_2 \end{align*} Write out the matrix-vector representation of this ...
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### Algorithm for min max of a function

I want to solve a problem of the form $$\min_{x \in X} \max_{y \in Y} f(x,y)$$ where $X \subset \mathbb{R}^d$ and $Y \subset \mathbb{R}^k$. Typically $d$ is large ($>100$) and $k$ is small (1-3)....
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### Is the function $y=xe^x$ invertible?

I'm wondering if the equation $re^r=se^s$ has any answer. If there is any answer,and $r=-1+v,s=-1-v$ in which $v$ is a positive real number,what can we say about $v$? Thank you in advance.
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### Determining N d-points yielding equal sums of Euclidean distances from M s-points

Given M source points (s-points), determine N, the number of destination points (d-points), and their locations (coordinates), such that the sum of the N Euclidean distances from each source point to ...
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### To solve this numerically : [closed]

$$0.5 = 1 −{0.955}^n − {0.005}^n{0.995}^{n −1}n − {0.005}^2{0.995}^{n −2}\left(\frac{n(n−1)}{2}\right)$$ I'm using MatLab but should I use a for-loop? Can anyone work me through the steps? Thank ...
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### How to mathematically model a realistic aperture illumination?

I want to know a mathematical expression that i can use to model a realistic aperture illumination to produce the primary beam of an antenna so that the radial distribution of this aperture ...
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### mathematical patterns and their connection to grouping “things”. [closed]

The heading of this is probably misleading as I know group has a well defined mathematical definition, yet I know not what it is. My question is very open ended, I hope you all don't mind. If we ...
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### Summation of n terms of a series$1+2+8+64+…$

In one of my problem , I got a series as $1$,$2$,$8$,$64$,$1024$...and so on. can we really get a sum expression for that series$???$ If yes, then what is the expression $f$ $?$ or the sum of $n$ ...
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### What do we call the harmonics in a discrete Fourier series representation?

In harmonic analysis using discrete Fourier series, if I'm using the 0f, 1f, 2f, 3f and 4f for representation where f = frequency, what is the correct way to say how many harmonics I'm using for ...
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### Write number as a power of 10

Just to clarify, I'm not interested in Standard Form/Scientific notation. Is it possible to write a number as a power of ten, so that for example it would look like this? ...
1answer
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### Given 3 random points, what is the probability of these two situations involving a perpendicular bisector and distances?

Suppose we're given 3 random points $p_0=(x_0,y_0),p_1=(x_1,y_1),p_2=(x_2,y_2)$ from a two-dimensional continuous uniform distribution $\{U(a,b)\}^2$, for some $(a\in\mathbb{R})\lt (b\in\mathbb{R})$, ...
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