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
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
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1answer
38 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
352 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 link)...
2
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2answers
167 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
41 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 ...
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0answers
58 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
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1answer
49 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 ...
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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?
-1
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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 $...
14
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0answers
168 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
197 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 ...
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2answers
276 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
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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 RootOf(_z^5+(2-4n)_z^4-10nx^3+(24n^2-16n-2)...
2
votes
1answer
82 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
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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
625 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
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0answers
36 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 d\...
2
votes
1answer
52 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
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0answers
36 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
99 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
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1answer
28 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
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
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1answer
83 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
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2answers
106 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 = x_{...
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 $x$,...
2
votes
1answer
133 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
94 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
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1answer
224 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
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0answers
80 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
43 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
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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 x}\left(v(x,t)...
5
votes
0answers
133 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. ...
2
votes
0answers
81 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
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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 $\{ H_{...
4
votes
2answers
102 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?
1
vote
1answer
299 views

Write two (or more) numbers as sum of multiples of other numbers (one, two or more)

I have the following problem: Numbers 32, 35 and 57 can be written as sum of multiples of 7 and 9: 32 = (7*2) + (9*2) 35 = (7*5) + (9*0) 57 = (7*3) + (9*4) Is ...
1
vote
1answer
58 views

How do I solve for the zeros of a Chebyshev polynomical? (on a computer)

I am working on a computer program and have a method that returns a number for a given $x$, $y$. So $f(x, y) = z$, where $f$ is my method. if I know $y$ and $z$, can I find what $x$ will be, without ...
0
votes
1answer
443 views

Probability of breaking the enigma cipher

I assume that most of you are already familiar with how the ENIGMA machine works, that the germans used during WWII. We now that the enigma machine has 3 scramblers with each 26 setting each. That ...
0
votes
1answer
32 views

Designing a Pushdown Automation to accept a language

Im a novice trying to understand the theory of computation.Im trtying to learn about PDA.I understand that it is a machine counterpart of CFG.Im basically referring to Introduction to Automata Theory ...
0
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1answer
61 views

Numeric calculation of partial derivative: proper sequence of operations?

I am calculating a second order mixed derivative by the following formula $$\frac{\partial^2 f(x, y)}{\partial x \partial y} \approx \frac{f(x + h, y + h) - f(x - h, y + h) - f(x + h, y - h) + f(x - h,...
1
vote
1answer
121 views

Can 2 items be added/taken away from a stack in push down automata at once?

Here is a language and 2 ways (I hope) of representing it with a PDA. Can I use the notation (b,a $\to$ ee) or anything of the like, to take away 2 items from the top of a list at once? Such as I ...
1
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0answers
331 views

Help with proving a language is regular (Sipser problem 1.49a)

I am working through Sipser's Introduction to the theory of computation on my own, so I don't have access to a teacher. Hopefully you can help me! Giving hints is highly appreciated. This question is ...
2
votes
1answer
33 views

Intersection symbols

I am writing a scientific paper. I need to express the intersection of two space, e.g. A and B where A and B can be a line, plane or a 3-D space. What is the appropriate symbol to state this concept. ...
3
votes
1answer
66 views

Hypercomputation & Higher Dimensional Variants of Conway's Game of Life

Conway's Game of Life is a simple and important mathematical game with some rules of evolution in a two dimensional space. It appears in many subjects in mathematics, artificial intelligence and ...
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0answers
167 views

Solution of equations involving determinant and matrix inverse

$x$ and $y$ are two scalar unknowns. The two equations are $$|\mathbf{I}+x\mathbf{h}_1\mathbf{h}'_1+y\mathbf{h}_2\mathbf{h}'_2|=R$$ and $$\mathbf{h}'_1\left(\mathbf{I}+x\mathbf{h}_1\mathbf{h}'_1+...
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0answers
189 views
-3
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1answer
58 views

how to do the opposite of mod in this equation

if $X=((A*Y)+C)\mod m$ how does one calculate $Y$? If you have all other variables except Y? I have already tried everything I can think of just don't know how to do the exact opposite of mod, I can ...
0
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1answer
50 views

How to take the integral of a derivative to obtain desired result?

I am aiming for the form of derivative below computed over time that causes its differentiated variable V to go from an initial -.001 and increase to reach 10. I will explain my current calcs below ...
0
votes
1answer
57 views

Numerically solve integral with a function as variable of integration

I want to use a function as variable of integration for example in evaluating the integral: $\int_0^1 e^{\cos x}f(\sin x)d\cos x$ in which $f(x)$ is an arbitrary function.