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Questions tagged [algorithms]

A description of the specific steps needed to solve a particular problem in an unambiguous way, expressed in an abstract form.

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1answer
133 views

Choosing hardware to use with PETSc

I would like to know more on choosing hardware to get the maximum price/performance when using the PETSc library (and various third-party preconditionners) I am currently working on a 2 cpu (2*E5-...
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0answers
83 views

Finding most efficient route (distance/number of nodes) that uses nodes at least X amount away from another node

I'm trying to find the "looped" route with the lowest value of D/n, where D=Distance, and ...
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2answers
924 views

How can calculations cause an arithmetic overflow even if the final value fits?

I am reading Algorithm Design Manual by Skiena, which says in Chapter 8, Section 8.1.4 when talking about the calculation of binomial coefficients: Intermediate calculations can easily cause ...
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1answer
190 views

Compute eigenvectors of a matrix with known eigenvalue spectrum

If I have already accurately known the eigenvalue spectrum (i.e. all eigenvalues) of a matrix, is there any efficient numerical algorithm to compute all the eigenvectors corresponding to these ...
4
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3answers
331 views

Propagating Schrodinger equation

My task is to simulate quantum evolution. To do that I need to perform this operation $$w = e^{-itH}v$$ where $H$ is a sparse matrix and $v$ is the initial column vector. I am wondering if there is ...
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3answers
237 views

Languages Speed [closed]

Suppose a program was written in two distinct languages, let them be language X and language Y, if their compilers generate the same byte code, why I should use language X instead of the language Y? ...
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1answer
32 views

Travelling Salesman Problem - where's the “return to city”-constraint? [closed]

I'm looking at your standard definition of the TSP.... (see wikipedia).... and in the statement leading up to the definition, it states that we must return to the city we began from. Which ...
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0answers
25 views

Using HMM for speech synthesis [closed]

I am trying to make a speech synthesizer using a Hidden Markov Model. I read the wikipedia page and several whitepapers and presentations (such as this one) but I am still not sure how this algorithm ...
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0answers
393 views

MCNPX for nuclear simulation [closed]

is it legal here to ask this problem? I need someone help. I run mcnpx. I try to calculate f4:n using nps:1000. But, it stop directly before culculate f4. There is comment: stack trace terminated ...
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0answers
119 views

HDF5 Many Writers, One External Reader

I have an application where I want to have 3 different machines writing to their own independent HDF5 files at a high rate, but have a way to read data from them externally and combine it. Is HDF5 a ...
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0answers
81 views

How to fix time intervals to store data in a stochastic simulation (continous time markov chain)

I am using FORTRAN to implement Gillespie's stochastic simulation algorithm. I would be running many simulations in parallel (both parallel instances with different seed and parallel functions); if I ...
4
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1answer
98 views

How to evaluate a series of derivatives?

Consider the function $$f(\mathbf{x}) = \sum_{n=0}^{N} a_n \left( (\mathbf{b}-\mathbf{x})\cdot \nabla \right)^n \frac{1}{r}$$ where $r = |\mathbf{x}| = \sqrt{(x-x_0)^2 + (y-y_0)^2}$ and $a_n$ and $\...
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3answers
165 views

Numerical integration algorithm for this set of ODEs

I have to solve numerically the following initial value problem, which physical origin is discussed in this article by G.I. Taylor (1941). Here $\eta$ is the independent variable and ranges beetween $...
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1answer
1k views

Newton iteration for cube root without division

It's a fairly well known trick to avoid division in calculating square-roots to apply Newton's method to finding $1/\sqrt{x}$, and probably better known, using Newton's method to find reciprocals ...
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0answers
79 views

Bracket Algebra, Straightening Algorithm

My apologies if the question is simple. I need to write a code for straightening algorithm. Which includes defining bracket algebra. I tried to write it in CoCoA-5, but it wasn't possible because ...
5
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3answers
173 views

Algorithms for radiation treatment planning

I have a medical physics problem - I want to maximise the dose absorbed by a brain tumour whilst minimising the dose in the rest of the brain, especially certain organs, such as the pituitary gland, ...
3
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1answer
79 views

How to Check a Hyper-Cube for Defects

I would greatly appreciate some help/references on solving the following problem: You are in charge of searching through a n-dimensional hyper-cube $[0,1]^n$ to make sure that it does not contain ...
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2answers
304 views

Faster methods for projecting a mesh onto a hierachally unrelated mesh?

I have a set of independent meshes whose results I would like to project onto another non-hierachally related mesh. Until now, I've been accomplishing this by finding the nearest-distance node in the ...
3
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1answer
264 views

Using SVD to biorthogonalize left and right eigenvectors?

I have a set of left and right eigenvectors from an nonsymmetric eigenproblem, and I'd like to biorthogonalize them. I tried Gram-Schmidt, but this fails for most cases. I then read that the SVD is ...
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3answers
618 views

Algorithm to compute the intersection of two lines given their cartesian equations

I'm looking for a way to compute the coordinates of the intersection of two lines. Each lines are defined with a point and a normal vector. We can assume than the normal vectors are not zero and ...
4
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1answer
257 views

Active Elements in Projected Newton's Method?

To those who are familiar with the projected Newton's method or projected gradient method... We consider a constrained optimization problem with simple bounds. Particularly, minimize f(x) subject to ...
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0answers
52 views

Finding a scalar field in order to generate a solenoidal vector from a given vector

I am working on generating a (complex) solenoidal vector field $\mathbf{A}$ from a prescribed (complex) vector $\mathbf{a}$ and the gradient of a scalar, $b$, such that $$\mathbf{A} = \mathbf{a} + \...
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2answers
141 views

How to prove time complexity of merge sort

I was asked to prove that the time complexity of merge sort is $ O(log_2n)$ but I cannot find a way to continue my method. Any help? $T(n)=2T(\frac{n}{2} )+n$ $T(n)= 2[2T(\frac{n}{4})+n] +n = 4T(\...
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1answer
113 views

MAX-SAT and MAX-cut

I have been using MAX-SAT solver to obtain the exact ground state of ising spin glass model: For 1D periodic model, for systems with 50 binary variables and interaction range of 15th nearest ...
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1answer
112 views

Help me analyze the computational cost of two kinds of operations

everyone, I have a question about computational costs for a algorithm. That is: I have two vectors $u_n,\ v_n\in \mathbb{C}^N$, a matrix $A\in \mathbb{C}^{N\times N}$ (can be both sparse and dense) ...
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1answer
1k views

Efficient way to compute the cumulative weights of all subtrees rooted at each node in a tree?

I have a tree data structure (rooted, unbalanced, with unbounded branching factor), where each individual node has an associated 'weight'. For every node $n$ in the tree, I'd like to compute the ...
3
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1answer
278 views

Computing the (non-convex) boundary of a set of paths between two points

I have a set of paths between two fixed points (marked in red below). Each of these paths consists of an ordered series of $\{x, y\}$ points (marked in blue). I am trying to find the ordered set of ...
2
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1answer
91 views

Adjusting Keplerian orbits for thrust with numerical stability

I'm writing a mod for a game that models orbital physics (Kerbal Space Program, or KSP). I'm attempting to model the effects of thrust on spacecraft in certain states where the game only models them ...
6
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2answers
948 views

A method to determine whether a point can be contained within a circle with no neighbouring points

I have been working on a particularly challenging problem and was hoping for some guidance. Here is my problem. I have a point cloud containing millions of points. For each point in the set, I need to ...
2
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2answers
112 views

fastest and most efficent way to count all combinations in many sets and sum them together

I am a Java programmer who has reached the limits of brute computer power. My relational database (and non relational databases) is not producing results quick enough and I have hit a bottleneck in ...
8
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1answer
243 views

Are there improved method of computing the following expression?

given a symmetric matrix $Y \in \mathbb{R}^{n \times n}$, and an arbitrary matrix $X \in \mathbb{R}^{n \times n}$, and a vector $v \in \mathbb{R}^{n \times 1}$, is it possible to compute the following ...
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1answer
214 views

What is the algorithm that matlab used in its built-in function 'pca'?

Do anyone know what is the algorithm that MATLAB used in its built-in function "pca"? I have the following data set: 148.9820 55.8438 210.2150 149.3030 56.8891 208.4280 151.4400 ...
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2answers
2k views

Patankar's algorithms for Numerical Heat Transfer and Fluid Flow

I am looking for the algorithm of Patankar (for example, SIMPLE, SIMPLER, SIMPLEC and PISO) written in Fortran for the simulation of heat transfer and fluid flow.
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1answer
50 views

What is a general method for identifying how connected parts of a binary volume are?

I have a binary volume consisting of a number of disconnected objects. (coming from a noisy, anatomic dataset) However, some of the objects are 'somewhat' connected. Picture a big cylinder and a ...
6
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1answer
999 views

How to get proper parameters of SPH simulation?

I'm implementing basic fluid flow simulator using SPH method basing on e.g. https://www10.informatik.uni-erlangen.de/Publications/Theses/2010/Staubach_BA10.pdf. EDIT (dead url): https://www10.cs.fau....
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3answers
308 views

Algorithm: Extracting motion frequency from video

I was wondering if anyone knows of any algorithms or projects that can detect the frequency of a motion from a video clip. Like if I had a video of a bouncing ball with constant frequency, could an ...
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3answers
513 views

Finding optimal velocity profile using Dynamic Programming

While continuously reading about Dynamic Programming I have a problem, implementing it in a practical application. Let's assume we want to optimize our way to school which we go daily by bicycle. ...
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2answers
666 views

Finding shortest path in a time/distance map

I get a distance map output after using a Fast Marching Method. The PDE involved is the Eikonal equation which take the form : $$\begin{cases} c(x).|\nabla u| =1\\ u(x) =\phi(x) ...
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0answers
248 views

Parameter ESTimation (PEST) algorithm? Steps and purposes? [closed]

I'm reading up on the Parameter ESTimation algorithm, (Link to PEST homepage 1), and having trouble understanding the broad strokes, as I keep getting lost in null spaces, different regularized ion ...
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2answers
103 views

How to measure trajectory regularity?

I have two animal running trajectories. A regular one with repeated back and forth running between point A and B, like the one on top in the figure. The other one is very irregular, animal paused and ...
1
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1answer
435 views

How to minimize the artefact of a cartesian to polar transform followed by a polar to cartesian transform?

I'm transforming cartesian images into polar images. (x,y) => (angle, radius) I fill the polar image by iterating on each of its pixels and filling them by doing the reverse polar transform. For a ...
4
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1answer
114 views

Numerically compute one-to-one mapping

I have a set of points defined by their coordinates $(x_1,y_1)$ after changing some parameters of the problem I obtain a second set of points defined by their coordinates $(x_2, y_2)$. There exists a ...
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1answer
97 views

Appropriate algorithm for (non-linear) ODE with integral equilibrium constraint: collocation?

I have a problem of the following structure: For some scalar $g$, functions $F(z)$ and $h(z)$ defined on $[0,\bar{z}]$ , and a non-linear operator $\phi(F,z)$ (in reality, $F$ and $h$ are vector ...
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1answer
60 views

Algorithm for distributing members over activites (with individual preferences)

So in my school we have a day where everybody participates in different activities. Each projects can have like 10 members. The whole day is divided in 2 or 3 different blocks, in which the pupils ...
0
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1answer
70 views

Finding roots without knowing much about the function

Consider solving numerically for roots: $( x_0, y_0): f(x_0, y_0) = 0, g(x_0, y_0) = 0$ where you only know that f, g continuously differentiable but the theoretical differentiation is not a ...
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0answers
77 views

Algorithm for optimizing graph interconnectivity

I have a partiuclar kind of graph problem and (not having a background in graph algorithms) I would like to know how this kind of problem is called in the literature and what algorithms exist for ...
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1answer
515 views

Why are Octrees used for Multipole space decomposition?

In most (all?) implementations of the Fast Multipole Method (FMM), octrees are used to decompose the relevant domain. Theoretically, octrees provide a simple volumetric bound, which is useful for ...
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1answer
232 views

How to compute the weight matrix for tomography applications?

I am trying to compute the weight matrix for a set of straight ray paths through a reconstruction region. Ideally, I would like to be able to do this for both a rectangular grid region, where each ...
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0answers
55 views

Algorithm to explore a 3D scalar potential

I have to write an algorithm/code to reconstruct an unknown 3D scalar potential $ V(\mathbf{r})$ up to a specified threshold $E_c$ (assume that the potential is monotonic) The problem has the ...
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1answer
1k views

What are the relative benefits of using Adams-Moulton over Adams-Bashforth algorithm?

I am solving a system of two coupled PDE's in two spatial dimensions and in time computationally. Since the function evaluations are expensive, I would like to use a multistep method (initialised ...