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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-2
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1answer
52 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
29 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
18 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
49 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
1answer
73 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
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?
3
votes
0answers
58 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
158 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
117 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
35 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
124 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
43 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
19 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
85 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
40 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
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 ...
0
votes
0answers
46 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
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
votes
1answer
173 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
52 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
27 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
vote
0answers
69 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
votes
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: $a^2+(1/(a-2))^2=4^2$
0
votes
0answers
37 views

Iterative algorithm for finding approximation functions for N-dimensional space

Say, I have billions of integral-valued vectors of the form $(0, 1, 3, 0, 0, 0, 3)$. My goal is to efficiently compute approximate distribution of values of each component of these vectors for each ...
0
votes
0answers
25 views

Mathematical models for self healing robotics

Does anyone know about any attempts to mathematically model self-healing (autonomous repair) robotics ? or any existing mathematical models about this ? When a robot or machine suffers from damage or ...
2
votes
0answers
45 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
votes
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? $$ f(x)=\frac{-x}{x^2-1} $$
0
votes
0answers
25 views

Simplify recursion function based on a matrix, real-world usecase

I have an auction running, and I'm trying to calculate the expected amount of first, second etc. places to be taken by a particular bid. To achieve that, based on historical data I make a following ...
2
votes
1answer
59 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 ...
0
votes
2answers
61 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 $b=\pi/2+8\pi$ ...
4
votes
1answer
77 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
votes
2answers
50 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
votes
1answer
124 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
vote
1answer
114 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
vote
0answers
32 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
votes
1answer
101 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 $(i,j)$.
1
vote
0answers
55 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
vote
0answers
28 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
votes
4answers
872 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
votes
0answers
102 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
vote
1answer
70 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?
0
votes
4answers
68 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
votes
1answer
124 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
votes
1answer
78 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
votes
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
votes
4answers
366 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
votes
1answer
28 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
votes
1answer
39 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 ...