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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1answer
70 views

Particle swarm optimization

I don't know where to start. Like, I don't know how to plug the info into the algorithm. Show two iterations of particle swarm optimization (neighborhood approach) method. Mathematically show two ...
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2answers
56 views

growth rate of n! versus $r^n$

How do you show that $\lim_{n\to \infty} {n!\over {r^n}} $ approaches $\infty$? the growth rate of $r^n$ is slower than $n!$, so the latter one is increasing faster, but how do you show the above ...
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4answers
940 views

Newton form vs. Lagrange form for interpolating polynomials

I'm just wondering, what are the advantages of using either the Newton form of polynomial interpolation or the Lagrange form over the other? It seems to me, that the computational cost of the two are ...
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0answers
17 views

I need help with this Standard Uniform random variable problem

Click here for problem image I need help on how to do b,c and d. Can I please have an idea of how to start it because i have no idea how to do this.
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0answers
51 views

The solution of Allen-Cahn equation?

$$\frac{\partial\phi(\mathbf{x},t)}{\partial t}=\varepsilon^{2}\Delta\phi-F^{'}(\phi),\ \ \ \mathbf{x}\in \Omega,t>0$$ $$\frac{\partial \phi}{\partial\mathbf{n}}=0\ \ \text{on} \ \partial\Omega$$ ...
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0answers
37 views

for what value of p does the integral converge

For what value of p does $\int_0 ^1 x^p dx$ converge? So I used improper integral value for this, looking at the result $$\lim_{p\to 0+} {1\over p+1}(x^{p+1}-p^{p+1})$$ *** I made a mistake, I got ...
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0answers
62 views

Find the different values of this integral when all paths of integration are possible

This is the question.. I only know how to do the question from infinity to infinity.. enter image description here Find the different values of this integral when all paths of integration are ...
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1answer
40 views

An unusual limit

I a reading an article in neural coding. It cintains a limit which I cannot understand. (It remindes the benomial sum but it didn't work for me) I am talking about $(22) \Rightarrow (23)$ in the ...
1
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1answer
155 views

Is there a word for an “infinite algorithm”?

According to Knuth's notes (see Slide 3), an algorithm, by definition, satisfies the following five properties: Finiteness: Terminates after a finite number of steps. Definiteness: Each step is ...
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0answers
46 views

Constructing triangulations algorithmically

I am developing a Python package for computations in algebraic topology (namely: cohomology and Massey products on manifolds). Basically all the stuff I'm doing requires an explicit triangulation of ...
2
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0answers
48 views

A recursive problem with GAP concerning lists and an iterator loop

I have the following question concerning a list algorithm in GAP: Let $L_1$ be a non-empty list with certain objects as entries. I wrote a program and called it helping_program_1. The Input for ...
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0answers
24 views

Algorithm detect simple curves using Voronoi diagram or Delaunay triangulation?

I wonder if there is algorithm/method to determine if closed (or even non closed) curve is simple or not, using the mathematics from the field of computational geometry? Especially I wonder if exist ...
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1answer
23 views

How can I find an approximation for y(1) using MATLAB without ODE solvers? (Euler's Method & Matrices)

Task: Given \begin{align*} y(t+h)&\approx \underbrace{\left(\begin{matrix}1-h & 5h & h\\3h & 1-h & 0\\0 & -th & ...
1
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1answer
43 views

Is there a good way to compute this integral?

Sometimes questions like: "How many digits does 2015! have?" become quite trendy. The most reasonable approach would probably use Stirling's formula. However doing this in the same way over and over ...
7
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1answer
549 views

Is there a way to calculate the definite integral of inverse of a 5th degree polynomial?

I want to calculate the definite integral of inverse of a 5th degree polynomial. The problem is that the inverse of the polynomial cannot be calculated (by using Matlab). However without calculating ...
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1answer
33 views

Find RHS from LHS.

$A=\left[ \begin{array}{cc} 0 & 1 \\ 1 & 0 \\ \end{array} \right]<==>\left[\begin{array}{cccc} 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 \\ 1 & 1 & 0 & 0 \\ ...
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0answers
42 views

Affine Matrix for Computer Graphics

I was given this assignment task which I have no idea where to start with so I'm hoping that someone can help me with this? Student A: Matrix 4x4 (0.989, 0, -0.148, 0, 0.018, 0.992, 0.121, 0, ...
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0answers
133 views

Finding The Radix of A Quadratic Equation

I have found previous solutions to finding the radix of a quadratic equation, where both of the provided roots return the same radix or base. However, unless I am some type of arithmetic error of ...
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1answer
21 views

Question related to the security of RSA method

I learned about the RSA method, where if B wants to send a message $M$, say $0 \leq M <n = pq$ to A with public key $(n,e)$, then B sends $M'= M^e (mod \ n)$. Then A can decode this message using ...
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0answers
14 views

adding a vertex and edges which do not change lengths of shortest paths (ACM ICPC problem)

I am trying to figure out how to solve the problem "Farm and Factory" from the ICPC archives. For the sake of making this question self-contained, I've reproduced the problem below: All hail ...
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0answers
58 views

What is meant by “deterministic error”?

I am reading a scientific paper in computer science and I have found the term of deterministic error. I googled to find any meaning to this notion but I did not find anything. So is there anyone to ...
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0answers
26 views

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, ...
1
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1answer
75 views

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 ...
1
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1answer
27 views

polynomials in terms of elementary symmetric polynomials

Let a polynomial of $2n$-variables be $$ f(x_1,\cdots,x_n,y_1,\cdots,y_n)=\prod_{i,j=1}^n(1+x_i+y_j). $$ Let the elementary symmetric polynomials be $\alpha_1=\sum_{i=1}^n x_i$, ...
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0answers
22 views

terms of taylor expansions of multiple variables at the origin

By the fundamental theorem of symmetric polynomials, $X_1,X_2,\cdots,X_n$ are polynomials of $ e_1,\cdots,e_n$ and $$ \mathbb{Z}[ e_1,\cdots,e_n]=\mathbb{Z}[X_1,X_2,\cdots,X_n]. $$ We define a ...
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1answer
435 views

Can I get multivariable taylor series expansion on wolfram alpha or matlab?

I need something like this : say $a, x, y$ and $t$ are three non-negative real numbers. Now define the complex number, $z = -y + i(a+x-t)$ and consider the function $f(x,y) = z\text{ }tanh (\pi z) log ...
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0answers
40 views

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 ...
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4answers
132 views

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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0answers
52 views

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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3answers
74 views

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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0answers
49 views

Represent Dirac Delta function in Finite Difference method

I recently solving $-\Delta u=\delta$ where $\delta$ is dirac delta function using FDM on 2 dimensional space. Since dirac delta function is undefined at origin, and 0 elsewhere, I will use ...
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1answer
28 views

Integration using Fourier Transform

How to integrate the function $(\sin x)^2/x^2$ using Fourier transform of function $g(x)=1$ if $|x|<1$ else $g(x)=0$ which is $(sin w/w)*2/pi$?!thank you in advance.
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0answers
28 views

Extended Transition Function Equivalent Proof

I encounter a difficult question (for me), and until now I haven't found a solution for it. In this question, I have to proof that these two are equivalent using induction. ...
0
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1answer
114 views

Open Composite Newton–Cotes formula

I'm after an Open Composite Newton-Cotes formula. The reason for this is I have a function that I know at N evenly spaced interior grid points but I do not know it at the two endpoints. I'm after ...
0
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1answer
29 views

efficient mathematica code to reduce computational time

I am trying to a code in Mathematica that is taking unacceptably long time (day) to run as it involves four summations. I am wondering is there any way to do some changes in the code so that it ...
0
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0answers
18 views

I need help with the Von Neumann Stability Analysis for this specific PDE

I've been working on this question $\frac{\delta u}{\delta t} = \frac{\delta^{2} u}{\delta^{2} x}-\lambda \frac{\delta u}{\delta x}$ where $\lambda = 3 $ After discretising the PDE I have ...
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0answers
19 views

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 ...
2
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1answer
29 views

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 ...
2
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0answers
54 views

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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0answers
23 views

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 ...
5
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4answers
707 views

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? ...
3
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1answer
177 views

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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0answers
18 views

how to find the total amount depends specific percentage

I have to find an easier way to find the net amount that makes the base amount after calculating the percentage. For example I have an amount of $70000$ and I want to know the actual amount that add ...
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2answers
38 views

How do I go about computing the distance between a point and a line in 4-D?

The point p = (1,1,1,1) ∈ R^4 (real numbers) to the line L(a) with a = (1,2,3,4) in particular. I tried it as follows: The distance d(p,L(a)) is the orthogonal projection of p onto L(a). So the dot ...
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2answers
46 views

How to solve the hypotenuse of a Right Triangle when the adjacent is unknown and the other leg is given?

I already know how to solve a hypotenuse when both leg and adjacent are given. But my instructor gave as an assignment which is to find the hypotenuse. The problem is this: One leg of a right triangle ...
12
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1answer
203 views

On the prime-generating polynomial $m^2+m+234505015943235329417$

In 2009, J. Waldvogel and Peter Leikauf found the remarkable Euler-like polynomial, $$F(m)=m^2+m+234505015943235329417$$ which is prime for $m=0\to20$, but composite for $m=21$. Define, ...
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0answers
31 views

data for zeros of the derivative of the Riemann zeta function

People have computed a large number of zeros of the Riemann zeta function. Do we have data for zeros of the first derivative of the Riemann zeta function?
0
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1answer
19 views

Fast Fourier transform with a different product function

Problem Given 2 N degree polynomials as $$a_0 + a_1x+a_2x^2+...+a_Nx^N $$ and $$b_0 + b_1x+a_2x^2+...+b_Nx^N $$ Assume no 2 coefficient are same in the 2 polynomials. Find the product of the ...
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0answers
118 views

Computing the density of a set of multiples

I have a finite* set $A=a_1<\cdots<a_r$ of positive integers. Define $B$ as the set of positive integer multiples of $A$ and $$ A_1=\frac{1}{a_1} $$ $$ ...
2
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3answers
69 views

Computing the tail of the zeta function $\sum_{n>x}n^{-s}$

I want to compute $$ f_s(x)=\sum_{n>x}n^{-s} $$ for some $s>1$ (in my case, $s=3$). Of course $$ f_s(x)=\zeta(s)-\sum_{n\le x}n^{-s} $$ but for $x$ large this is hard to compute. Are there good ...