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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1answer
60 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
265 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
1answer
95 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 ...
2
votes
1answer
62 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
168 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
132 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
99 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 ...
48
votes
4answers
4k 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, ...
3
votes
1answer
164 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
25 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
38 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 ...
0
votes
2answers
82 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
29 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
100 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
49 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
1answer
37 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 ...
3
votes
3answers
349 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
160 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
40 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
56 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
48 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
26 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
1answer
44 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 ...
13
votes
0answers
163 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
186 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
2answers
248 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
65 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
76 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
86 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
602 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
35 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 ...
2
votes
1answer
50 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
21 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
34 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 ...
3
votes
1answer
90 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
25 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
vote
0answers
21 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
76 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 ...
1
vote
2answers
105 views

Floating-point arithmetic error

Suppose you need to generate $n + 1$ equally spaced points on the interval $[a, b]$, with spacing $h = \frac{b-a}{n}$. In floating-point arithmetic, which of the following methods: $x_0=a$, $x_k = ...
0
votes
1answer
127 views

Min exponent range in normalized floating-point system

In a floating-point system with precision $t = 6$ decimal digits, let $x = 1.23456$ and $y = 1.23579$. (a) If the floating-point system is normalized, what is the minimum exponent range for which ...
2
votes
1answer
121 views

Using inequalities to find vertices of a polytope

Consider a set $C$ of vectors of integers $x\in\mathbb N^d$ satisfying $$ \begin{align} \forall\ i=1..d & \ \ [0 \leq \ell_i \leq x_i \leq u_i]\\ \forall\ i=1..d-1 & \ \ [x_{i+1} \leq x_i] ...
4
votes
5answers
90 views

A equation of Trigonometry

hello dear friends please help me to solve this problem.Thanks very much. How much are $a$ and $b$ in the problem below? $$1-2\cos 3a +2\cos 3b=0$$$$1-2\cos 5a +2\cos 5b=0$$
0
votes
1answer
172 views

Generalized eigenvalue problem for symmetric, low rank matrix

I'd like to solve a generalized eigenvalue problem of the form: $$\mathrm{A}x = \lambda \mathrm{B}x$$ $$s.t. x_i^T\mathrm{B}x_i=1.$$ Where $\mathrm{A}$ and $\mathrm{B}$ are symmetric but low-rank ...
2
votes
0answers
75 views

An elliptic curve for the multigrade $\sum^8 a_n^k = \sum^8 b_n^k$ for $k=1,2,3,4,5,9$?

I. The first solution to, $$\sum^6_{n=1} a_n^9 =\sum^6_{n=1} b_n^9$$ $$13^9+18^9+23^9-5^9-10^9-15^9 = 9^9+21^9+22^9-1^9-13^9-14^9$$ was found in 1967 by computer search by Lander et al. It stood ...
0
votes
1answer
39 views

Interpreting high p value and low correlation value

I am trying to run regression on financial data in R. I am new to regression analysis so I am finding it to difficult to interpret certain scenarios. I have the code as follows: Regression analysis ...
0
votes
0answers
48 views

Finite Difference Approach for the 1D Conservative Advection Equation with Spacially Varying Velocity

I am attempting to numerically solve the following conservative advection equation in 1D, using a finite difference method. $\frac{\partial}{\partial t}u(x,t) + \frac{\partial}{\partial ...
5
votes
0answers
118 views

A summation involving the ceiling function

I'm trying to find a better method of calculating the sum $$\sum_{k=1}^N\lceil ak\rceil^2$$ where $a$ is an irrational number. So far, my only idea is to somehow use a best rational approximation. ...
1
vote
0answers
76 views

Is there any efficient progam or software to calculate the fractional chromatic number?

The fractional chromatic number $\chi_f(G)$ is a generation of the chromatic number of a graph $G$. It can be formulated as a linear programming question: Let $\mathcal{I}(G)$ be the set of all ...
5
votes
0answers
185 views

A property of the subgroups lattices

Let $G$ be a finite group. Consider all the subgroups $H$ such that its subgroups lattice $\mathcal{L}(H)$ is distributive (i.e. the group $H$ is cyclic, by Ore's theorem), and among them, let $\{ ...
4
votes
2answers
99 views

How to solve this least square problem effectively?

I want to solve the least square problem, $\min\|Ax-b\|_2$, but the condition number of $A'*A$ is very large, How can I solve this problem effectively?