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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20 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 ...
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0answers
24 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 ...
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1answer
28 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 ...
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1answer
40 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 ...
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1answer
21 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 ...
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1answer
14 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 ...
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1answer
26 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 - ...
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0answers
30 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 ...
5
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1answer
362 views

Cylinder-ray intersections equation

I found an article involving infinite cylinder-ray intersections, and I don't know how they develop this equation: $$(q - p_a - (v_a, q - p_a)v_a)^2 - r^2 = 0$$ In the end of the first page I quote: ...
10
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1answer
287 views

Krylov-like method for solving systems of polynomials?

To iteratively solve large linear systems, many current state-of-the-art methods work by finding approximate solutions in successively larger (Krylov) subspaces. Are there similar iterative methods ...
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0answers
15 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 ...
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1answer
565 views

Fast methods to check linearity of differentials? Generalizing linearity?

The L1 Mat-1.1010 -course here has taught me the linearity conditions $f(a x)=a f(x)$ and $f(a+b)=f(a)+f(b)$. I want to generalize it, some quite irrelevant slow investigation here. It requires time ...
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0answers
19 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 ...
26
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3answers
8k views

What algorithm is used by computers to calculate logarithms?

I would like to know how are logarithms calculated by computers. The GNU C library, for example, uses a call to the fyl2x() assembler instruction, which means that ...
2
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1answer
13 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. ...
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0answers
25 views

How to solve a second order ODE numerically with two boundary conditions at different points?

I can only find Runge-Kutta method in textbook to solve the equation numerically with boundary conditions like y(0)=$\alpha$, y'(0)=$\beta$, but how can I solve it with a bounday condition like ...
3
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1answer
316 views

Software for numerical solution of a non-linear ODE system?

I have been given a nonlinear system of ODEs which has arisen out of a colleague's engineering research: $$\begin{array}{rcl} \dot{x}_0&=&x_1\\ ...
2
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2answers
47 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 ...
3
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1answer
39 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
39 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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1answer
33 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?
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1answer
39 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 ...
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1answer
21 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 ...
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0answers
12 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 ...
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1answer
30 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.
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0answers
33 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 ...
2
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2answers
174 views

Galois group command for Magma online calculator?

I need to test if a family of 7th deg and 13 deg equations are solvable. I'm new to Magma, so my apologies, but what would I type in, http://magma.maths.usyd.edu.au/calc/ to determine the Galois ...
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2answers
326 views

Minimum number of iterations in Newton's method to find a square root

I am writing an algorithm that evaluates the square root of a positive real number $y$. To do this I am using the Newton-Raphton method to approximate the roots to $f(x)=x^2-y$. The $n^{th}$ iteration ...
2
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0answers
33 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
44 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
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3answers
98 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 ...
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0answers
15 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 $t\in[0,1]$, ...
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0answers
47 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
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0answers
22 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
101 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 $\varepsilon$ ...
5
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9answers
6k views

Fastest Square Root Algorithm

What is the fastest algorithm for finding the square root of a number? I created one that can find the square root of "987654321" to 16 decimal places in just 20 iterations (I'm not ready to release ...
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0answers
16 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 $A$. ...
0
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1answer
29 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 ...
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0answers
21 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
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0answers
33 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 ...
0
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1answer
36 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 ...
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0answers
16 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
58 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 + ...
5
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3answers
274 views

FFT with powers of 3

Classic Fast Fourier Transfrom (FFT) works fine, when $n$ is power of 2. How to generalize FFT procedure when $n$ is power of 3? Is it possible to easily modify the algorithm and preserve its ...
5
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1answer
137 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 ...
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2answers
193 views

The J programming language: is it useful for mathematics?

I just stumbled upon the J programming language, which has the description: J is particularly strong in the mathematical, statistical, and logical analysis of data. It is a powerful tool in ...
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1answer
49 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 ...
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0answers
22 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? $\displaystyle y=\frac{cos(s_n)-cos(s_{n+1})}{sin(s_{n+1}-sin(s_n)}(x-sin(s_n))-cos(s_n)$