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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2
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3answers
29 views

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 ...
1
vote
1answer
20 views

Entropy Calculation and derivation of logarithm

I have probabilities as $$p_1 = 0.4,\ p_2 = 0.3,\ p_3=0.2,\ p_4=0.1$$ hence entropy is given by: $$H(x) = -\big(0.4\cdot \log_2(0.4) + 0.3\cdot \log_2(0.3) + 0.2\cdot \log_2(0.2) + 0.1\cdot ...
0
votes
0answers
18 views

Maximize polynomials

Hi guys I need some help. I am reading a paper and I cannot understand something simple. The author has 4 polynomials with a constrain and is trying to find the optimal solution to the problem. ...
0
votes
1answer
53 views

What are the minimal mathematical prerequisites for starting to study Artificial Intelligence? [on hold]

This question is really broad as there are many aspects to the AI research. However, I just need a bare minimum of prerequisites that will allow me to approach any sub-field of the AI (coupled with ...
0
votes
0answers
34 views

If a computer can check 1 million colorings per second, about how long would it take to check all possible three-colorings on 100 vertices?

If we imagine a graph G with 100 vertices, how would we find all possible colorings for G if G(v) = 100? I think that to solve this problem we would start with vertex 1 with 99 edges for the first ...
2
votes
1answer
52 views

Prove that sets don't intersect

I am trying to solve a computer algorithm problem that boils down to solving the following. I would appreciate some mathematician assistance on the proof. So here goes: Having: Set $S$ - rational ...
1
vote
1answer
19 views

How to find the order of accuracy of this implicit RK method (using Taylor series)?

I want to get the order of accuracy (local truncation error - LTE) of this implicit 2-step method. The first step is Backward Euler to determine an approximation to the value at the midpoint in time, ...
0
votes
0answers
19 views

Convergence of the Midpoint (Leapfrog) method when applied to $u'(t)=\lambda u(t)$?

So, I am trying to solve this question: where example 7.7 can be found here: http://i.stack.imgur.com/PVCIC.png My approach: Forward Euler (FE) method is given by: ...
0
votes
1answer
25 views

Locally evaluate nonlinear dynamic system's stability using eigenvalues

I don't have a large mathematical background, but I'm working with Computational Neuroscience. I have a large Synaptic Matrix (x axis: presynaptic NeuronID, y axis: postsynaptic NeuronID) in a Modular ...
-1
votes
0answers
30 views

fast computation of complete elliptic integral matlab

I'm using matlab to compute complete elliptic integrals of first ($K$) and second kind ($E$). I'm having an issue with computational speed evaluating these integrals using matlab function ...
1
vote
1answer
23 views

Pollard Rho intuition

I have been reading about pollard rho factorization, however their is something I don't understand if we don't use a polynomial that is pick two random numbers and see the gcd(a-b,n) > 1 if it is ...
1
vote
0answers
51 views

Counting problem of combinations of symmetric matrix.

Given, a symmetric $n*n$ matrix $G$ with 0,1 entries. Each row of has same number of 1. $G$ is arranged in a certain order using a rule. The rule is described below- $G$ is partitioned in to two sub ...
4
votes
1answer
103 views

Sums of three cubes in arithmetic progression equal to a cube $x^3+(x+y)^3+(x+2y)^3 = z^3$

Using exhaustive search, small positive and primitive integer solutions to, $$x^3+(x+y)^3+(x+2y)^3 = 3 x^3 + 9 x^2 y + 15 x y^2 + 9 y^3= z^3\tag1$$ are, $$x,y = 3,1,\quad x+y =2^2$$ $$x,y = ...
1
vote
1answer
19 views

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 ...
46
votes
4answers
3k views

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, ...
2
votes
1answer
29 views

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 ...
1
vote
0answers
22 views

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 ...
0
votes
0answers
12 views

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 ...
1
vote
2answers
53 views

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 ...
1
vote
0answers
20 views

Simpson's rule is not good enough for the best approximation in L2 problem

The problem came from my computation methods (practice) class. It was to write a program which does the following: Original problem statement: We have a [0; 1] segment. Let us divide it into $2^n$ ...
-2
votes
1answer
77 views

(x,y) coordinates from gluing together a sequence of right triangles with arbitrary angles [duplicate]

I have been scratching my head all day over this question for one of my assignments. I haven't made any progress and I'm at the point of giving up. Here's what I need help with. Start by gluing ...
1
vote
1answer
45 views

is it possible to find $x$ where $y$ is equal to a whole number in a non iterative fashion

Given the equation $$\frac{635x+326}{637+x} = y$$ where $$x>0$$ Is it possible to find all positive values of $x$ (there is only one) where $x$ is positive and $y$ is a whole number. While I ...
0
votes
0answers
6 views

Fourier Analysis of a p2 continous Galerkin Scheme for the Laplace & Poisson Equation

Background: I am obtaining residual calculations for the 3D Laplace and Poisson Equation using finite element continuous galerkin scheme with lagrange polynomial basis functions for p1, p2, p3 and ...
0
votes
0answers
35 views

does any polyhedral partition admit a convex piecewise quadratic surface defined over?

Given a polyhedral partition, i learnt that there exist some conditions for the existence of a convex piecewise affine surface over this partition for example the following study. ...
0
votes
1answer
16 views

Golden Section Search termination condition

From textbooks I found that the tolerance for Golden Section Search method should be set to $\sqrt{\epsilon}$, where $\epsilon$ - is the machine epsilon. This can be derived from Taylor series. So, in ...
0
votes
0answers
19 views

Computational verification request

Let $I(x) = \sigma(x)/x$ be the abundancy index of $x$. Note that $\sigma$ is the classical sum-of-divisors function. Previously, I computed for $u$ in the inequality $$\sqrt{3} < ...
3
votes
3answers
286 views

A bug with the WolframAlpha computational search engine?

I think I may have discovered a bug with WolframAlpha. So I was trying to determine all $x$ such that $$\sum_{i=0}^{5}{x^{-i}} < \frac{13}{12}.$$ WolframAlpha spit out $x > 13$ (see this ...
2
votes
2answers
55 views

How to calculate the errors of single and double precision

We consider the initial value problem $$\left\{\begin{matrix} y'=y &, 0 \leq t \leq 1 \\ y(0)=1 & \end{matrix}\right.$$ We apply the Euler method with $h=\frac{1}{N}$ and huge number of ...
0
votes
1answer
29 views

Determining the Change in a variable as a function of change in independent variables

I have an Equation at hand: F = V/P I'd like to find out that for a given number of unit change in F, how many units of change are due to change in V and how many units of change are due to change ...
1
vote
0answers
23 views

Determining an unknown Function

I have an interesting operational situation at hand. I have a dependent variable, let's call it variable Y and a set of independent variables: V, H, N. (relationship is based on my operational ...
0
votes
1answer
32 views

Simple way to find square root of perfect squares

Let me first explain my problem: I am trying to write a program that can generate operations that compare a set of data rather than pulling from a list of possible relations. I have it to the point ...
1
vote
0answers
18 views

Find largest regions bounded by a set of planes

Suppose we are given a set of planes that partition the unit cube into a large number of regions. Is there a computationally efficient way to find the region with the largest volume?
0
votes
0answers
12 views

Automated tool for an algebraic problem

I have a polynomial $f=1+y_1y_2+y_1x_1$ over $GF(2)$. Now variables $y_1,y_2$ are my control but not $x_1$. Hence if put $y_1=1$ and $y_2=1+x_1$, polynomial $f$ will be zero. Similarly I have a ...
0
votes
1answer
41 views

Natural Numbers and $A_x=\{y \in A \mid y \leq x\}$ [closed]

Suppose A is a arbitrary subset of Natural Numbers and $A_x=\{y \in A \mid y \leq x\}$ with respect to $ n \in A \Longleftrightarrow n \in A_n $ and $A_n$ is finte, which of them is True? a) A and ...
10
votes
0answers
100 views

Product of primes mod n

Let $n$ be an odd composite number. I'm trying to compute $$ f(n)=\prod_{n/2<p<n}p\pmod n $$ where $p$ ranges over the primes in the indicated region. Can this be done (significantly) faster ...
2
votes
1answer
82 views

Why does Archimedes Method to calculate Pi decrease in precision after a certain time?

i`m using the following recursive formula to calculate Pi based on Archimedes ideas. $$ S' = \sqrt{2-\sqrt{4-S^2}} $$ The formula gives back the edge length of a Polygon B based on the edge length of ...
0
votes
1answer
75 views

Computation complexity with simple algebra expression reduction

I'm watching this computer science video on computational time complexity of a function where they introduce some maths and it doesn't make sense to me. I'm not even sure what the name for this maths ...
0
votes
2answers
44 views

finding the roots of polynomial of degree 5

I want to find the roots of $f(x)=x^5+(2-4n)x^4-10nx^3+(24n^2-16n-2)x^2+(20n^2-6n-1)x-16n^3+4n^2+4n$ with maple, but with solve(f=0,x); it give me ...
2
votes
1answer
43 views

Algorithms for generating $A_n$ and $S_n$ from specific generators

Is there a simple algorithm to generate the elements of the alternating group $A_n$ in terms of some small set of generators? For example, when $n = 4$, I'm looking for an algorithm whose output is a ...
1
vote
1answer
75 views

How to obtain a convergent solution iteratively for a linear system of equations?

I am working on a problem that requires an iterative procedure to solve a linear system of equations, the system of equations in matrix form is: $$\underbrace{\begin{bmatrix} r_{11} & r_{12} ...
0
votes
1answer
89 views

How to evaluate growth of input size from n to 2n in this case?

This is the question I am currently working on What is the effect in time required to solve a problem when you double the size of the input from n to 2n, assuming that the number of milliseconds the ...
0
votes
0answers
15 views

Divisors of a number in a given range

I'm working on a problem and wondered if there was a clever way to do it. The general form of the problem is like this: given $\ell_1,\ell_2,$ and $N$, find all divisors $d$ of $N$ with $\ell_1\le ...
1
vote
0answers
28 views

Is there some database or software to look for patterns in polynomials?

Like if I am looking at these polynomials, $$x^8-8x^6+20x^4-16x^2+3$$ $$x^{10}-12x^8+48x^6-72x^4+33x^2$$ $$x^{12}-16x^{10}+88x^8-192x^6+138x^4$$ And I want to know if they are members of some ...
0
votes
1answer
19 views

What are the solutions of the following exponential inequality for $n \in \mathbb{N}$?

What are the solutions of the following exponential inequality for $n \in \mathbb{N}$? $$n^3 < 4^{{(2n - 1)}^8}$$ I tried using WolframAlpha, but only an Inequality plot is returned, which I do ...
2
votes
0answers
25 views

Good method for finding roots that *usually* fall within an interval?

I've been using Brent's method to find the roots of a monotonic, nonlinear, non-differentiable function. The roots often fall within a known interval, but Brent's method fails if they occasionally ...
0
votes
0answers
40 views

How to Solve this Implicit Equation

Let $Y$ to be a uniformly distributed random variable. Consider function $z(\gamma)$ defined by the following equation. $$ \int_{\left\{y\in(0,1), -\frac{\log ...
3
votes
1answer
52 views

Simple factorials

I've been doing some work with factorials and the normal way of calculating them is simply not working so well. When the numbers get really big, doing iterative multiplications is not viable and gets ...
1
vote
1answer
16 views

Formula for maximal usage

I'm a programmer with a way to easy question for this site, please correct me if I'm wrong. I have the following given: ...
1
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0answers
19 views

after hajek, can we guarantee that annealing has reached a solution in the best 1%?

hajek showed in http://web.mit.edu/6.435/www/Hajek88.pdf that there are conditions under which an annealing process is guaranteed to find the global minimum. these constraints are pretty tight, but ...
1
vote
1answer
44 views

Stopping criterion for approximating exponential series

Given $e^{x}=1+x+\frac{x^2}{2!}+\frac{x^{3}}{3!}+\cdots $. Summing in the natural order, what stopping criterion should you use? Can you rearrange the series or regroup the terms in any way to get ...