# Questions tagged [computational-mathematics]

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

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### Calculation of special subsets in high-dimensional binary matrices

I need to solve a rather specific problem related to binary matrices. The task is to count the number of specific "combinations", where "combination" means the following: this is ...
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### Looking for a description of "Ostrowski’s square root technique"

While eagerly searching for iterative methods to approximate $f(x)=0$ (commonly known as root-finder) for the quantile function or probit, I stumbled over "Ostrowski’s square root technique"....
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### Higher Dimensional Spherical Harmonics in Cartesian Form

Are there any tables in the literature or computer software for computing higher dimensional spherical harmonics in Cartesian form, like this Wikipedia article, which lists them for three dimensions. ...
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### Fast way to calculate (AAᵀ)⊙(BBᵀ)

I need a computationally efficient way to calculate $AA^\top \odot BB^\top$, where $A$ and $B$ are tall, real-valued matrices of the same size ($\text{nrows} \approx \text{ncols}^3$) $\odot$ stands ...
20 views

### Reformulate an algorithm as a sequence of standard matrix operations

Consider the following code snippet ...
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### Adequate Root Finder To Compute The Quantile Function

The cumulative distribution function of the standard normal distribution $\Phi(z)=\displaystyle\frac{1}{\sqrt{2\pi}}\int_{-\infty}^z e^{-t^2/2}dt$ cannot be expressed in terms of elementary functions, ...
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1 vote
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### Probability distribution of exponential chickens

This problem originates from minecraft chickens. Let's say I start with one ( fully grown ) chicken. This chicken lays one egg every $\left[5, 10\right]$ minutes, ...
1 vote
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### Solve problem path of resistance stochastically stable equilibria

I'm working on Stochastically stable equilibria bout Evolutionary Game theory. In the famous paper by Peyton Young there is an example of a matrix 3x3 with the solution of the paths less resistance. I ...
1 vote
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### Domain Truncation Error for Semi-Infinite BVP

Suppose I have a BVP defined on a semi-infinite domain, of a form that looks something like $$N[f] = 0 \\ f(0) = a \\f'(0) =b \\ f'(\infty) = c$$ where $f$ is some (generically nonlinear) third order ...
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### Finding the coordinate of four points of imaginary intersecting lines which passes through end points of two intersecting lines

image I want to find the coordinates of the points A,B,C,D where two imaginary lines intersect each other, where this imaginary lines passes through the end points of the two lines L1 and L2, the ...
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### Benchmark Neural Networks on High-Dimensional Functions

For a personal project, I am interested in benchmarking certain neural network architectures in the context of high-dimensional function approximation. Specifically, I am interested in continuous, ...
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### Book Recommendations for Learning Python for Mathematics.

Lately, I've been finding that I often need to compute various things and graph some pretty complicated functions. I've realized that learning to program, especially in Python, could be really helpful ...
1 vote
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### Generating Equation for randomisation of a long sequence for finding pairwise distance repeats

I am not mathematician. I am making a python code. I am generating a equation to do permutation. We want to analyze repeats in one sequence of pairwise distance and randomize it and calculate the ...
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### Correlation vs Regression for a simple task

Hello everyone and thank you for taking the time with my issue! I want to apologize in advance if my question would've fit better on stack exchange, but I decided that the question is more related to ...
1 vote
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### Is there a website that can locate the nearest triangle center from a point? [closed]

In this question, I conjecture that the sequence of points will converge Given $A_1= (0,0), \ B_1=(11,2), \ C_1(3,5)$ , $C_{25}(3.3556952569262, 2.9821465573228)$ which should be very close to the ...
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### Clarification Needed on Potential Function Term in Discrete Klein-Gordon Equation Transformation

I am studying the PhD thesis Dynamics of nonlinear lattices: asymptotic behavior and study of the existence and stability of tracked oscillations and I have observed a mistake at a function on page 69....
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### Closest edge to a rectangle in a plane of rectangles

I have a 2D plane (with discrete points) that contains arbitrary-sized rectangles and all rectangles are axis aligned. I have their coordinates (upper-left) and sizes (length and breadth). Suppose I ...
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### Numerically solving the Advection-diffusion equation with no-flux boundary condition results in violation of mass conservation

I am trying to solve numerically the advection-diffusion equation of the following form $$\frac{\partial C}{\partial t}=\alpha\frac{\partial^2 C}{\partial x^2}+\beta \frac{\partial C}{\partial x}$$ ...
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### Simplest prime test algorithm possible: what's its complexity?

We got the brute force algorithm: Input: natural number $n$. Set $k_{i+1}=k_i+1$, $k_0=2$, $i=0$ If $\frac{n}{k_i}$ is an integer, return $'\mathrm{Composite}'$, else, set $i=i+1$. If $k_i^2\leq n$ ...
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### Correctness of algorithm to find the number of elements of order $x$ in Symmetric Group $n$?

To find the number of elements of order $x$ in $S_n$ Generate all possible partitions of $n$ by divisors of $x$. For each partition, check if the LCM of the part lengths matches $x$. Calculate the ...
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### Derivation of Q in EM algorith

Trying to learn EM Algorithms. Can someone explain the derivation steps they took to go from step 4.1 - 4.3. I am quite new to computational stats and it feels like I may be missing some fundamental ...
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### Beautiful errors in graph of $\sin(x^2+y^2)$

I was writing a simple program to help visualize inequalities based on 2 variables. The test inequality that I was using was this: $$\sin\left(0.1(x^2+y^2)\right)\geq0$$ Regions that satisfy the ...
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### If a matrix is an outer product of two vectors; can I determine the vectors? [closed]

I am working with floating point numbers. There is a 3x3 matrix that has determinant 1e-14. I have reason to believe this matrix is an outer product of two vectors. If the assumption is correct, how ...
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### Hardy-Littlewood maximal function algorithm

There exists implemented algorithm which compute the Hardy-Littlewood maximal function at least for reasonably simple non-trivial cases? E.g. piecewise linear functions?
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1 vote
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### Is there a way to find if there relationship of numbers

I have a challenge. This may be little tricky or even not possible but wanted to check if anyone has any thoughts on this? PS : This question is in general and not related to only to R. May be I can ...
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### verifying Ramanujan constant

The famous Ramanujan constant $e^{\pi \sqrt{163}}$ is a near-integer. see the link here. I tried to calculate this number with matlab and failed. Matlab cannot even deliver the first 9 apparently ...
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### Is it possible to find something better than binary search for this problem?

Let's say we have $n$ urns (numbered $1$ through $n$) and the first $k$ urns have a ball in them (for some $k$ unknown to us) and the remaining urns are empty. Our goal is to determine $k$ by looking ...
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### Fast solvers for saddle-point problem (linear system)

I would like to speed up my multi body simulator. There, in every time step a linear system, often referred to as saddle-point problem, has to be solved. The system looks like this  \begin{bmatrix} ...
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Assume I have a variable u, which is an $m\times n$ array filled with exclusively real values. I want to find the maximum value within this ...