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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5
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46 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. ...
4
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0answers
64 views

Finding every $n$ such that $n\times$ ('reverse' number of $n)=m^2$ such as $1584\times 4851={2772}^2$

Let $r(n)$ be the 'reverse' number of $n$ in the decimal system. For example, $r(1234)=4321$. Then, here is my question. Question : Can we find every $n(\in\mathbb N)$, which is not a square ...
4
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0answers
311 views

“Green Globs” question

When I was in high school geometry, we had a fun little game on the computer called Green Globs (the website for the software is http://www.greenglobs.net/index.html). A number of targets (globs) are ...
4
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0answers
514 views

Obtain a contradiction

Motivation : The motivation is to show that the equation $x^{2b}.x^{2a} +(3-x^{2b}) x^{a} + (1-s^2)=0 $ has no solutions in integers for any values of $x,b,a,s$ ( choosen as per the constraints ...
3
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0answers
25 views

Has there been work on computational group theory applications to computing colimits of crosses n-cubes of groups?

I'm trying to compute homotopy groups of a few spaces using crossed n-cubes of groups. I'm able to describe a few colimits in terms of quotients of induced crossed modules and nonabelian tensor ...
3
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0answers
70 views

Computing the decomposition of a representation of $S_n$

I have an explicitly defined representation of the symmetric group that I would like to decompose into irreducibles. How to do this most easily? The best approach I have so far is as follows: Find a ...
3
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0answers
51 views

Algorithm for primary decomposition of ideals in a power series ring over a field

Let $K$ be a field such that there exists an algorithm for factoring a polynomial over $K$ into the product of irreducible polynomials. For example, the field of rational numbers $\mathbb{Q}$ is such ...
3
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0answers
138 views

$\pi$, disjunctive numbers, and finite sequences of given length

It is an open problem whether the number $\pi$ is disjunctive in base $10$, i.e., whether every finite sequence appears (at least once) in the base $10$ expansion of $\pi$. Of course, every sequence ...
3
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0answers
52 views

Supremum over unitary group action

Let $A$ and $B$ are two given Hermitian operators on matrix algebra $M_n(\mathbb{C})$. $A$ is positive semi-definite with unit trace. I want to know the general method for calculating the following ...
2
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0answers
30 views

Tool for construction of graph with specified properties

Is there a tool (class of algorithms for graph generation) that can construct graph with specified properties. E.g. construct graph who is homeomorphic with both to K5 and K3,3. Construct planar graph ...
2
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0answers
37 views

A Free Boundary Problem

Is there any special way to solve such a problem. Any idea would be appreciated. At least does anybody know which method is useful to solve this problem numerically? Is it even solvable numerically? ...
2
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0answers
38 views

Computer program to simplify formulas

What is the computer program that attempts to simplify sums of binomial coefficients, factorials, etc.? Possibly Zeilberger wrote it, but I'm unsure. If so, possibly it was talked about in his A=B ...
2
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0answers
39 views

Quantitatively comparing event trains of different lengths for Poissonness

I have a parameterized, effectively black box process that generates a series of events (simulated action potentials). Different parameter values often lead to different numbers of events. How can I ...
2
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0answers
202 views

Two-layer Perceptron for XOR

I'm reading Neural Networks for Pattern Recognition by Christopher M. Bishop. It's for a physics class, but I think the problem is closer to mathematics so I'm asking here instead of PSE. Chapter 4 of ...
2
votes
0answers
47 views

LLL and factoring polynomials in $\Bbb Z[x]$

Given a degree $2k$ reducible polynomial $f(x)=\sum_{i=0}^{2k}a_ix^i\in\Bbb Z[x]$ with $gcd(a_{2k},\dots,a_0)=1$ that is known to be of the form $f_1(x)f_2(x)$ with $deg(f_i(x))=\frac{deg(f(x)}{2}=k$ ...
2
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0answers
57 views

The Command “TzGoGo” in GAP

I am learning GAP and would like to ask one question about a command called "TzGoGo": If $P$ is a finite presentation of a group $G$, then will the eventual result of the command "TzGoGo(P)" be ...
2
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0answers
118 views

Using GAP to compute the abelianization of a subgroup

Let $K$ be the group generated by four elements $x_1,\cdots,x_4$ with relations that each generator commutes with all its conjugates. (An equivalent relation is, any simple commutator with repeated ...
2
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438 views

Solving large, sparse system of linear equations

I have a system of linear equations as follows: $$(A+I)x=B$$ where $I$ is the $n\times n$ identity matrix, $A$ is a $n\times n$ matrix such that the first and last rows are blank, and, for every ...
2
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0answers
90 views

Solving a particular system of Diophantine equations in $n$ variables (Frobenius equations)

I have a particular system of linear Diophantine equations in $n$ variables for which I need to find all nonnegative integer solutions. Specifically, they are Frobenius equations, meaning the ...
2
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0answers
34 views

Computing a particular finite set of quaternion matrices.

Let $B = \left(\frac{-1,-11}{\mathbb{Q}}\right)$ be a choice of quaternion algebra ramifying at $11$ and consider the maximal order ...
2
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0answers
250 views

How to convert a hologram into an image?

Suppose one knows in full detail the phase and intensity of monochromatic light in a plane. This is basically what a hologram records, at least for some section of a plane. By using this as the ...
2
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0answers
383 views

Logistic regression algorithm in Casio and Texas Instruments calculators

When using logistic regression on a Casio or Texas Instruments calculator, the output is of the form $$f(x) = \frac{c}{1+ae^{-bx}} $$ The problem I have (when teaching in a class where both types of ...
2
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0answers
66 views

is there a computationally efficient formula for computing the mutual information between two continuous variables?

I need to compute the mutual information between two continuous variables. Below is an equation shown to compute the mutual information between a variable $X$ and $Y$. $I(X;Y) = \int_Y \int_X ...
2
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0answers
398 views

Clarification on different types of solutions: analytical, closed form, iterative, algorithmic,

When doing computation, there are different types of solutions: analytical, closed form, iterative, algorithmic, exact, approximate, ... (there are probably more than I just listed and please don't ...
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0answers
21 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 ...
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0answers
48 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. $H$ cyclic), and among them, let $(H_{i_1})$ be the sequence of ...
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0answers
32 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 ...
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0answers
57 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 ...
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0answers
38 views

Is there any direct method for Lagrange multiplier based domain decomposed problem?

In elastic problem, we often solve K * u = f, where K is the stiffness matrix, f the external force vector and u the displacement vector. I'm trying decompose the mesh to domains, using Lagrange ...
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0answers
29 views

How to estimate the local error and the global error for Runge-Kutta method

How to estimate the local error and the global error for Runge-Kutta method in practice? I have no idea. I recieved a nice answer on the question at other site
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0answers
17 views

Metaprogram and Metametaprogram with BLOOP

I'm solving one question and have a problem. Problem is this: Imagine $f(x)$ in the following way. We give an input $x$ to a BLOOP program $Π$ , which prints out another BLOOP program $Π_x$. Then ...
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0answers
59 views

Finishing a problem using equalities

This is my problem: Let $a$, $b$ and $c$ be positive real numbers with $abc=1$. Prove that $$\frac{a^{n+2}}{a^n + (n-1)\,b^n} + \frac{b^{n+2}}{b^n + (n-1)\,c^n} + \frac{c^{n+2}}{c^n + ...
1
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0answers
23 views

Use of Matlab to put equation into vector form

Is there a way to put the following equation of a line into vector form using Matlab? $\displaystyle y=\frac{cos(s_n)-cos(s_{n+1})}{sin(s_{n+1}-sin(s_n)}(x-sin(s_n))-cos(s_n)$
1
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0answers
33 views

Solving many independent non-linear systems simultaneously

I'm working on solving lots of systems of nonlinear equations. Luckily, the non-linear equation is the same, but the parameters are different: $$ f(\vec{x}_0; c_0) = 0\\ f(\vec{x}_1; c_1) = 0\\ ...
1
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0answers
29 views

How to reconstruct geometric object that a Frobenius group acts on

A Frobenius group has equivalent definitions: a transitive permutation group on a finite set such that no non-trivial element fixes more than one point and some non-trivial element fixes a point. ...
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0answers
45 views

Setting up Kernel to Numerically Solve Fredholm Equation of Second Kind

I am looking to confirm if what I am doing is the proper procedure. I writing a program to discretely solve a Homogeneous Fredholm Equation of Second Kind that is set up as follows: $ \int ...
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0answers
21 views

Transformation between Ideal and Warped Surface

I work on manufacturing metal panels with holes drilled in them. Suppose I have an ideal 3D surface from CAD. I want to compare it to the actual part using reference points to compare between the two. ...
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0answers
55 views

Time needed to algebraically solve system of $15$ nonlinear equations with parameters

How long can I expect it will take to algebraically solve a system of $15$ nonlinear equations (without any numbers, only parameters), if I feed it into a computing software? I'm asking for symbolic ...
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0answers
168 views

Nerve Theorem: Is the finite union of closed convex sets triangulable?

My Question: Let $A_1, \ldots, A_k \subseteq \mathbb{R}^n$ be closed convex sets. Is the union $\bigcup_{i=1}^k A_i$ triangulable$^1$? If so, why? Background: I'm trying to better understand the ...
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0answers
52 views

QR decomposition: Same results for Classical Gram-Schmidt and Modified Gram-Schmidt

I am implementing QR decomposition (in Fortran) for a complex-valued matrix, using Classical Gram-Schmidt and Modified Gram-Schmidt (and Householder). I was expecting that the Classical Gram-Schmidt ...
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0answers
437 views

Change MATLAB code from Lax-Wendroff to Leapfrog

I want to see how leapfrog would look using this code, but I'm having issues implementing it. I think my biggest problem is adding in the $ U_j^{n-1}$ term, I just don't get the logic. Here's what ...
1
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0answers
31 views

Generating N-dimensional points acording to given distribution

I searched here on Math.SE and haven't found anything that was exactly what I was looking for, so I'm posting it here. If there is anything, pardon my ignorance. I thought it was my first post here, ...
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0answers
29 views

Find allowed error of an argument regarding the allowed error of a function.

To what precision can $x$ be obtained with logarithmic table (with $5$ digit table) if $x$ lies between $300$ and $400$? Any ideas?
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54 views

What exactly is 'computer mathematics'?

I'm looking at some potential things to study next semester and I see a full B.sc. degree called 'Computer mathematics'. It says it's a hybrid between computer-science and mathematics. Does anyone ...
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0answers
91 views

Lamé's equation - elliptic PDE?

I have a specific PDE in 3-dimensional space + time (the right one). u(x,t) is the unknown function (values are in R^3) and F(x,t) the right hand side, mu and lambda are positive constants. Now ...
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0answers
28 views

Nonlinear optimization using parallel input/output

I have a system that accepts a vector and returns a function value. The goal is to change the elements of the vector such that the function value is minimized using a derivative-free solver, eg. using ...
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0answers
16 views

Tools for optimizing asymptotic bounds.

Is there any tool for this task ? Given the asymptotic bound in term of $n$ and other paramaters $t_1,\dots,t_r$, then return the value for each $t_i$ which optimizes the expression in term of $n$, ...
1
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0answers
128 views

Simpson's rule characteristics

I just wanted to ask a quick question in regards to simpson's rule for integration. I have been reading up on the trapezoidal rule, and have found the notations and have an understanding such that: ...
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0answers
25 views

Model to reward adaptative communication

I'm currently working in different simulations focused on the study of artificial evolution of communications in robots, and I have stumbled against the problem of its mathematic formulation. The ...
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0answers
185 views

Power sums, fast algorithm

I know some schemes to compute power sums (I mean $1^k + 2^k + ... + n^k$) (here I assume that every integer multiplication can be done in $O(1)$ time for simplicity): one using just fast algorithm ...