# 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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### How do computers generate primes so quickly?

From what I understand, when a computer encrypts a file using an encryption standard like RSA, one of the steps is to generate two large primes, and multiply them together. I have created RSA keys on ...
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### Computing as many digits as possible of $\sqrt{2}$ with a pen and a paper in 5 minutes

You have to compute as many digits as possible of $\sqrt{2}$ with a pen and a paper (an eraser if you're lucky...) in 5 minutes. What will you do? What is your justification for doing it? The ...
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### Unknown variable in formula - binomial coefficient? [duplicate]

I'm currently researching a filter and don't quite understand one of the equations used there, since it contains a variable I don't know how to calculate: $$(1)\,\,a^{m, k}_s = \frac{c^{k, m}_s}{m^k}$$...
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### deconvolution of exp($x^2$)

I would like to know whether we can get the function of type exp($x^2$) by convoluting any functions. That is which function convolution gives exp($x^2$). Thanks in advance
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### computing a fixed interest rate

I've been struggling for hours now with understanding a Topcoder problem, Autoloan , but i cannot grasp the way of computing it from a mathematical point of view. The excerpt goes as follows: A ...
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### Analytical expressions for the orthogonalization of a specific set of vectors

I would like to know whether analytical or closed-form expressions could be obtained for the orthogonalization of a set of vectors in the following setting. Let $x_t$ be a vector indexed as a time ...
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### Calculate height for rows of rectangles within a given width

I have an array of rectangles, all of the same height, but with different widths. Imagine they are on a single line with a uniform gap between them as shown below... |XXX| |X| |XXXXX| |XXX| |...
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### Can car traffic be managed by mathematical formula? [closed]

How car traffic is managed? Is it managed by mathematical algorithm? Or by human(operator)? If it's by operator, can it be managed mathematically? Or is it by physics? By what theories/formula? ...
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### What is transpose multiplier and forward multiplier?

For linear system X = A*s, we define the forward and transpose multiplies Af and At as follows: Af = @(s) A*s; At = @(s) A'*s; I want to know what is forward ...
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### Simplifying the Generalized Eigenvalue Problem

Let $\Sigma_1$, $\Sigma_2$ be symmetric positive-definite real $n\times n$ matrices. We want to solve the generalized eigenvalue problem $$\Sigma_1V=\Lambda\Sigma_2V,$$ where $\Lambda$ is the ...
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### Using Orthogonal Collocation to solve Coupled Ordinary Differential Equations

I am trying to solve six first order coupled ODE's, two of these are associated with a heat balance of a catalyst pellet, and four are mass balances. I have been trying to solve these equations using ...
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### Prime numbers distribution theorem

I'm trying to understand Gauss' theorem: $$\frac{\pi(x) }{x/\ln x} \to 1$$ for large $x$. I've taken the list of first 1000 prime numbers from Utah university site, saved them to file ...
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### periodic boundary conditions and the FEM

I am trying to set up the mass matrix for a 1D system which I want to solve using finite elements. So the mass matrix is defined as $$M = \int{NN^T}dL,$$ where $N$ is the finite element linear ...
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### How to make Poisson voronoi diagram

I am facing a problem as follows : I want to make poisson voronoi diagram & for this I have to appropriately choose some generating points. Sources on internet(WIKI) refers that these points have ...
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### Calculate pairwise cosine distance only returning the lower triangular matrix

I have a matrix, where each row is a feature vector. I would like to find out the pairwise cosine distance between all of these feature vectors. The cosine value between all rows in a matrix could be ...
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### Special properties in the direct solving of sparse symmetric linear systems

In the area of computational solving of large sparse linear systems, some solvers specialize only on symmetric sparse matrices, be it positive definite or indefinite as compared to general (non-...
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### Consider the recursively defined language, L2

Consider the recursively defined language, $L_2$ i) $x \cap L_2$ and $y \in L_2$ ii) if $w \in L_2$, then so is $wxw \in L_2$ Find all strings in L_2 with length less than $7$ characters (...
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### Logistic Regression - malty classification

I want to understand why the probability of P(D|p) is presented as a product of mentioned probabilities. I read a lot of texts, but everywhere the explanations are full of terminologies to confuse the ...
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### What are the next few “tetranacci-like” pseudoprimes?

Starting with $n=0$: $k=2$ Given the roots $x_i$ of $x^2-x-1=0$. Then, we have the Lucas numbers, $$A_n = x_1^n+x_2^n = 2, 1, 3, 4, 7, 11, 18,\dots$$ The $n$ that divides $A_n-1$ are all the ...
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### Let $x$ be an integer and $n$ be a positive integer. Find the smallest $n$ such that $x^4+n^2$ is not a prime for any $x$.

I need help proving the following: Let $x$ be an integer and $n$ be a positive integer. Find the smallest $n$ such that $x^4+n^2$ is not a prime for any $x$. I know that the smallest $n$ is 8 by ...
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### Essential Prime Implicants and Minterm Expressions

I have an exam for a university course shortly, and upon reviewing one of my assignments I have come to realize that I don't understand why I have lost marks/how to do a couple of questions. Hopefully ...
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### Is “A New Kind of Science” a new kind of science?

A couple of years ago I was reading "New Kind of Science" (NKS) by S. Wolfram, and it presented lot of interesting ideas for a young Physics undergraduate. Now that I am studying Mathematics however, ...
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### How do I find the sum of first N numbers common to 2 APs?

Here is the question - Certain numbers appear in both arithmetic progressions 17, 21, 25, ... and 16, 21, 26, ... . Find the sum of first 100 numbers appearing in both progressions. The ...
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### numerically solving linear integral equations

I want to solve a 3*3 linear equation system but the equations are integral equations and he coefficients of solutions are to be extracted NUMERICALLY from some other integrals.I do not know how. I ...
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### Norm (modulus) of the derivative of complex function and Newton Method

I am implementing a function that approximates a root of a complex function, say $f(z)$. As we know, at iteration $i$ we ave $$z_i = z_{i-1} - \frac{f(z_{i-1})}{f'(z_{i-1})}$$ The division of ...
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### If negative of negative (--) = positive then why not positive of positive(++)= negative

As per my understanding positive and negative are just indicative of direction of number axes with zero at the center. If that is the case we should apply same laws to both positive and negative ...