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.

learn more… | top users | synonyms

2
votes
1answer
21 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
77 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
13 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 ...
0
votes
0answers
14 views

Embedding an Implicit Runge-Kutta Algorithm

I am interested in implementing a fourth-order RK method with variable step-size. However, in order to test for accuracy, the solver needs to periodically utilize a higher-order method to see if the ...
0
votes
1answer
19 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
41 views

High dimensional Differential Evolution

I want to minimize a cost function with Differential Evolution (DE) algorithm and I have 55 unknown parameters as an input for DE algorithm. Therefore, the DE should search in high-dimensional space ...
0
votes
0answers
24 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
45 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
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 ...
1
vote
0answers
47 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 ...
4
votes
2answers
84 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?
0
votes
0answers
22 views

How to calculate p-value using an algorithm on R assuming that distribution is unknown.

For a given sample x, where x is distributed with a normal distribution mean known but variance unknown. I am testing the hypothesis that variance is equal to one or greater than 1. The question is to ...
2
votes
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 ...
1
vote
1answer
33 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
41 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
34 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
23 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
votes
1answer
32 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 - ...
1
vote
1answer
51 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 ...
0
votes
0answers
23 views

Approximation for uniform load on parabolic cable along its arc length

I am doing analysis for cable structures. Let's say that the cable stretches from point A to point B and carries a vertical ...
0
votes
0answers
33 views
1
vote
0answers
30 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
14 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
42 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 ...
1
vote
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 ...
0
votes
0answers
34 views
-4
votes
1answer
40 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
votes
1answer
23 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
0answers
14 views

Mix of two bivariate distributions (two correlations hidden in data)

We have two sample vectors $X$ and $Y$ which are realizations (observations) of metric (continuous) random variables, and are interested in a sample correlation between them. Actually, a correlation ...
0
votes
1answer
32 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.
1
vote
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 ...
1
vote
1answer
35 views

Polynomial representation of intersection of polynomials

How to minimally represent intersection of two degree $d$ polynomials intersecting at $d^2$ points as a single polynomial?
2
votes
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? ...
0
votes
1answer
53 views

intersection of an ellipsoid and cylindrical plane.

I need to understand if an ellipsoid and a cylindrical arc intersect, what will be the general equation of the cutted ellipse? How can I solve for that equation? I know in 3D, the equation of an ...
3
votes
3answers
104 views

Formal notion of computational content

In constructive mathematics we often hear expressions such as "extracting computational content from proofs", "the constructivity of mathematics lies in its computational content", "realizability ...
0
votes
0answers
17 views

Efficient way to compute the strong convexity modulus of a function?

I have a strongly convex function $f:X\to\mathbb{R}$, where $X\subseteq \mathbb{R}^n$, with strong convexity parameter $\sigma>0$. By definition $f$ satisfies, for all $x,y\in X$ and $t\in[0,1]$, ...
0
votes
0answers
59 views

Double integral involving Dirac delta

I came across a problem in which I have to computationally evaluate an expression like this: $\underset{\vec{r}}\int{F(\vec{r}) \delta(\zeta)\,dx\,dy}$ where $\delta(\zeta) = 1$ over a curve ...
1
vote
0answers
28 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
0
votes
0answers
104 views

The Runga-Kutta method with a adaptive step

I have some questions about this method. I use Richardson extrapolation for select a adaptive step [Solving Ordinary Differential Equations I - Nonstiff Problems 167-168p]. What mean $\varepsilon$ ...
0
votes
0answers
17 views

Is there a software package to solve large (128 x 128) non-positive-definite quadratic programming problems?

I am trying to solve a quadratic program of the form maximize $\sum_{i=1}^n\sum_{j=1}^nA_{i,j}w_iw_j$ subject to $\forall i:w_i\ge 0$ and $\sum_{i=1}^nw_i=1$ for a 128$\times$128 matrix $A$. ...
2
votes
2answers
61 views

How does mathematics fit into fractal generation for computer graphics?

I have to do a research paper on any mathematical concept. The mathematical concept must be complex, so I thought fractals would be a good choice (I was told it was a complex idea). I have been ...
0
votes
1answer
30 views

Pumping Lemma for a regular language

I've done pumping lemma proofs in the past but I'm honestly not even sure where to start on this problem. Using the Pumping Lemma for Regular Languages show that the language $$L = \{a^i b^j c^k ...
0
votes
0answers
23 views

Which boundary condition dominates in elliptic boundary value problem?

I am working on a solution to a boundary value problem (which is too complicated for me to reproduce here) but have a question about the boundary. In many dimensions, my function is infinite along ...
0
votes
0answers
35 views

Why is the order of the difference operator defined as $p$ rather than $p+1$ for the second order differential equation by multistep methods?

I am reading the book Discrete Variable Methods in Ordinary Differential Equations (1962) by Peter Henrici. I am confused about the accuracy definition in multistep methods for the second order ...
1
vote
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 ...
1
vote
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 + ...
0
votes
1answer
37 views

Does 2 one-dimensional intervals touch?

As the title mentions I have 2 one-dimensional intervals given like so: $[a, a-b]$ $[x, x-y]$ where $a$ and $x$ are the start points, and $b$ and $y$ are the length of the intervals. The intervals ...
5
votes
1answer
140 views

Efficient free alternative to *Mathematica*

I am searching for a free alternative to Mathematica. By efficient, I mean that it should have every (or at least almost every) function that you can find in Mathematica, including for example Number ...
0
votes
1answer
50 views

Assertions about measures with computers

Let's consider the Lebesgue measure ($\mu$) over the closed interval $[0,1]$. As you know, $\mu(\mathbb{Q} \cap [0,1]) = 0$. In other way, as far as I know the computer just can represent accurately ...
1
vote
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? $\displaystyle y=\frac{cos(s_n)-cos(s_{n+1})}{sin(s_{n+1}-sin(s_n)}(x-sin(s_n))-cos(s_n)$