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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137 views
-3
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1answer
54 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
33 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
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1answer
53 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
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1answer
103 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
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1answer
38 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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0answers
66 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
242 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
136 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 ...
1
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0answers
62 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
3
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2answers
123 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
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1answer
45 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
27 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 ...
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0answers
18 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 + ...
0
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1answer
40 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
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1answer
187 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
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1answer
53 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
34 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? $\displaystyle y=\frac{cos(s_n)-cos(s_{n+1})}{sin(s_{n+1}-sin(s_n)}(x-sin(s_n))-cos(s_n)$
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0answers
92 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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2answers
47 views

If $a+(1/(a-2))=4 $ then $(a-2)^2+(1/(a-2))^2$ is .

If $a+(1/(a-2))=4 $ then $(a-2)^2+(1/(a-2))^2$ is . Note: $a^2+(1/(a-2))^2=4^2$
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0answers
46 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 ...
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2answers
45 views

Will the Newton's method be convergent to the root of the following function: $f(x)=\frac{-x}{x^2-1}$?

Will the Newton's method be convergent to the root of the following function, if the starting point $x_0>1$ will be chosen? $$ f(x)=\frac{-x}{x^2-1} $$
2
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1answer
66 views

Graph pruning whilst ensuring connectivity

Problem: I have a graph (in this instance, it's represented by a matrix which is $\in \mathbb{R}^{n \times n}$). In the raw graph, all nodes are connected to every other node (except themselves) in ...
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2answers
69 views

Numerical integration tolerance pitfalls

Consider that we want to estimate $$\int_{\pi/2}^{\pi/2+8\pi}sin(x)dx$$ (the value of this integrate is obviously zero) with the Midpoint rule. We start with the endpoints $a=\pi/2$ and $b=\pi/2+8\pi$ ...
3
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1answer
102 views

Defining a subgroup of $GL(2,7)$ in GAP

Considering this resent post in which $|G|=42$, I am thinking of making this subgroup concrete in GAP environment. Maybe, if the structure of $G$ was known then, we would use an appropriate mapping ...
2
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2answers
51 views

Difference between the complex roots of $f(x)$ and $|f(x)|^2$

I suppose a basic question, but it's causing me more problems than I envisioned! I have some polynomial $f(x)$ for which the roots are complex, $x+iy$. How will these roots change if I now take ...
0
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1answer
165 views

Overflow and underflow of a probability value

I am evaluating the probability that the minimum of a process is a above a a barrier $\log(H)$. The probability is given by $$P_i=1-\exp\left(-2\frac{(\log(H)-x)(\log(H)-x_b)}{\tau\sigma^2}\right).$$ ...
1
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1answer
146 views

Calculating the Average Number of Games Required to Reach a Theoretical True Elo Skill Rating from a given Initial Elo Rating

The USCF uses the following formula for Elo rating adjustments: $$R'=R_0+K(S-E)$$ $$E=\frac{1}{1+10^{(R_n-R_0)/400}}$$ Where $R'$ is the new rating $R_0$ is the initial rating $K$ is a ...
1
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0answers
39 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. ...
0
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1answer
151 views

How to discretize mixed partial derivatives?

How to discretize $\frac{\partial^3 f}{\partial x\partial y^2}$ at mesh point $(i,j)$? We should use mesh points which are nearest to $(i,j)$.
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0answers
64 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 ...
1
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0answers
31 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. ...
8
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4answers
897 views

What is the most efficient way to calculate the sine of a rational number?

I'm happy that we can use some trig identities like $$\sin\left(\frac{\theta}{2}\right) \equiv \pm \sqrt{\frac{1-\cos(\theta)}{2}}$$ and $$\sin(\alpha \pm\beta) \equiv \sin(\alpha) \cos(\beta)\pm ...
0
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0answers
125 views

Implementing formula correctly in matlab for neuroscience: total soma membrane potential?

Please help me to understand: am I correctly implementing a total soma membrane potential (TSMP) equation in Matlab? Due to being a new member I need to use this list link to refer to the links ...
1
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1answer
85 views

Isomorphism between two magmas with one.

Do we have a method to find one (or all) isomorphism between two given magmas with one using GAP? Edit If we have Loop or Latin square (with one) instead of Magma then do we have the method?
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4answers
82 views

Min and Max of $ f(x,y)=\frac{x-y}{a-x-y}$

I'd like to find max and min of $$ f(x,y)=\frac{x-y}{a-x-y}$$ where $0\le x<y\le a/2$. Any one can suggest? Thank you
3
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1answer
160 views

How to numerically solve the eigenvalues of the laplacian in a triangular domain with Dirichlet boundary condition?

Consider an arbitrary triangle. Now impose the Dirichlet boundary condition. How to solve the eigenvalues and eigenvectors of the Laplacian $-\nabla^2 = - \frac{\partial^2}{\partial x^2} - ...
4
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1answer
108 views

GAP code to get Multiplication Table.

I have a finite set $S=\{0,1,2,\ldots,n-1\}$ and binary operation $\star$ on $S$ defined by $$x\star y= \left\{ \begin{array}{l l l} \frac{3(x+y)}{2} ~~\text{modulo} ~~n& \qquad \mbox{if $x$ ...
0
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1answer
72 views

what is the coefficient of following expression

what is the co-efficient of $x^{50}$ in the expansion of $$\frac{1}{(1-x^{1.7})(1-x^{1.8})(1-x^{2.6})(1-x^{3.0})(1-x^{4.0})(1-x^{6.7})(1-x^{7.5})(1-x^{8.2})}$$ can you please explain me the logic
18
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4answers
410 views

How could I improve this approximation?

In a computer application, I need to solve trillions of times an equation which can be reduced to $$f(x)=\sin(x)-a x=0$$ Newton methods (quadratic and higher orders) are used for the solution. ...
0
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1answer
47 views

What is and what are the use for an “ AINV preconditioner ” or “ SAINV ”?

In an article that I'm reading there is a mention to this "thing" and I absolutely don't know anything about it, for me it could be anything. I noticed that this thing is somehow related to the math ...
0
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1answer
45 views

Converting x number of petaFLOPS into a base 2 number

I would like a few different formulas or methods for doing a couple of conversions and calculations: 1) How can I convert petaFLOPS into a base $2$ number representing how many operations per second ...
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0answers
64 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 ...
7
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2answers
190 views

How was the $3x+1$ problem checked up to $5 \times 2^{60}$?

The Wikipedia article for the Collatz conjecture states that: The conjecture has been checked by computer for all starting values up to $5 \times 2^{60} \approx 5.764 \times 10^{18}$. It gives ...
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2answers
485 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 ...
0
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1answer
63 views

Numerical evaluation of a complex integral

I have to evaluate numerically $f(z)$ via the Cauchy representation (so via a complex integral), in other words, I have to calculare $f(z)$ performing a complex integral: $\dfrac{1}{2\pi ...
0
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1answer
47 views

Change of variables in function $T(n)$.

I've been given this recurrence to solve: $T(n) = T(\sqrt n) + \theta(lglgn)$ And I'm told that the way to solve it is to let $m = lgn$, so that the recurrence can be rewritten as follows: $S(m) = ...
3
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1answer
176 views

Changing streams in PhD

I've a masters degree from a reputed Indian university in pure mathematics, with a specialization in Algebraic Number Theory. However, I'd like to apply for a PhD in computational math/theoretical ...
1
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1answer
74 views

minimize distance

consider a two dimensional system. two points are given whose co-ordinates are $(h1,h2)$ and $(k1,k2)$. I want to minimize the distance between these two points with the condition that person has to ...