Questions tagged [algorithms]

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

102 questions with no upvoted or accepted answers
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101 views

Finding the smallest root of a function on $[0, \infty)$

I would like to find the smallest real root of a 1-D real-valued function $f(x)$ on the domain $x\in [0,\infty)$. In this problem, I can make the following guarantees on $f$: $f$ does have a root at ...
5
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0answers
72 views

Efficient way to find eigenvalues of complex symmetric matrix with real off-diagonal elements

My goal is to find all eigenvalues (and eigenvectors) in a given range of magnitudes of a complex symmetric matrix with real off-diagonal elements (only diagonal elements are complex). Currently I'm ...
5
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0answers
65 views

Padua-type pointset for functions singular on line $x=y$

The Padua points $\mathrm{Pad}_{n} \subset [-1,1]^{2}$ are a unisolvent pointset with optimal growth of Lebesgue constant, described in detail here. With some work they can be used to generate a ...
5
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0answers
2k views

Two-chordless cycle extraction from a failed comparability graph recognition

I have implemented a comparability graph recognition algorithm from M.C. Golumbic's "Algorithmic graph theory and perfect graphs" book. It is hinted in Fekete, Schepers, and van der Veen's "Exact ...
4
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0answers
83 views

What Derivative-free optimization method should I use when my initial guess is very good?

I am trying to minimize a function where my initial guess is quite close to the minimum. I'm trying to minimize $$f(q) = \text{angle}(qw_1q*, v_1) + \text{angle}(qw_2q*, v_2) + \text{angle}(qw_3q*, ...
4
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0answers
109 views

Stable computation of $\log\sum x_i$ from $\log x_i$, with many terms

Kahan's summation algorithm is a method to compute sums: $$\sum x_i$$ with many terms, without significant error. I want to do this with very large numbers, and instead of the numbers themselves, I ...
4
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0answers
97 views

FFT-based Image Rotation Algorithms More Accurate Than Chirp-Z?

We're currently using a Chirp-Z based implementation: R. W. Cox and R. Tong, "Two- and three-dimensional image rotation using the FFT," IEEE Trans. Image Processing, vol. 8, no. 9, pp. 1297–1299, Sep....
4
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0answers
234 views

Sound Waves Simulation in 3D Environment

I want to do a simulation of sound waves including wave propagation, absorption, and reflection in 3D space. I did some research and I found this question in stackoverflow but it talks about ...
3
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0answers
65 views

Computation of Troullier-Martins pseudowavefunctions

The computation of Troullier-Martins pseudowavefunctions has been described in [1]. The pseudowavefunction $R^{\textrm{PP}}_l$ is defined by $$ R^{\textrm{PP}}_l(r) = \left\{ \begin{array}{ll} R^{\...
3
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1answer
95 views

How to find a pair of divisors as close as possible to each other?

For a given integer $n\in\mathbb{N}^*$, I want to find a pair $(x,y)\in{\mathbb{N}^*}^2$ such that $x*y=n$ and $|y-x|$ is as small as possible. A naive algorithm I found is : ...
3
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0answers
85 views

First order methods for a large scale semidefinite program

I am interested in solving the following semidefinite optimization problem: \begin{equation} \begin{split} \underset{X,\lambda}{\rm maximize} \;\;\;\;&\lambda^Tc \\ &-\mathbb{I} \le X \le \...
3
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0answers
93 views

Fast Algorithms for the Simplicial Decomposition of a Convex Polytope in N-Dimensions

I'm in the process of constructing an algorithm which computes the Voronoi diagram of a set of points, but I now need a method to decompose each Voronoi cell into simplices. The information we have is:...
3
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0answers
301 views

Open source implementation of Multiscale Combinatorial Grouping

I would like to use Multiscale Combinatorial Grouping for my PhD research. However, I am restricted to use open-source implementations and this one runs on Matlab. Does anyone know of an equivalent ...
3
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0answers
102 views

How can I evaluate the accuracy of my n-body simulation?

I am making an n-body simulation in python. There are many different methods to numerically solve the system of differential equations governing the gravitational interactions between the $n$ ...
3
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0answers
81 views

Computing Algebraic Riccati inequality

In my Robust model control, I have got a couple of quadratic Riccati inequalities which need to be solved numerically on MATLAB. My question, Is there function on MATLAB can solve quadratic Riccati ...
3
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0answers
207 views

logsumexp with one very large term and many very small terms

I want to compute an expression of the form: $$L = \ln\sum_i e^{x_i}$$ Suppose that there are many small terms, say $e^{x_i} \approx \epsilon$. If there are $N_\epsilon$ such terms, their ...
3
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0answers
106 views

Find a function's minimizing set of parameters

I have a function defined by three parameters (or variables): $f(a,b,c)$ This function is not explicitly defined but is actually a piece of code which returns the result of fitting a curve $g(a,b,c)$ ...
3
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0answers
98 views

Dissipation and symplectic manifolds

I'm working on an API for simulation of port-Hamiltonian systems. As far as I understand it, a Hamiltonian system is symplectic if it is power conserving, and so including resistive elements would ...
3
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0answers
76 views

Parallel algorithm to use in place of PORTA?

We currently use PORTA software to find the list of facet-defining inequalities (FDI) for polytopes that we work with. For certain polytopes, PORTA works fine. But because it is a serial algorithm (...
2
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0answers
24 views

Alternatives to breadth-first-search in 3D grid cluster detection?

I've got a question about a good way to find the quickest algorithm for my problem: problem: I've got a 3D cubical grid containing voxels that are either 1 or 0. It is stored as a flattened array. If ...
2
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0answers
40 views

Evaluating integral $F(r_2) = \frac{1}{r_2^n} \int_0^{r_2} r_1^n f(r_1)\ \mathrm{d}r_1$ without growing instability

I have the following expression to be numerically integrated in a vector-based library (e.g. numpy, MATLAB, etc), $$ F(r_2) = \frac{1}{r_2^n} \int_0^{r_2} r_1^n f(r_1)\ \mathrm{d}r_1, $$ where $n$ is ...
2
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0answers
157 views

What exactly is the cause(s) of blow-up for too-large step size in a method like RK4?

I have been working on creating a few home-made numerical methods, and I am using them to visualize text-book problems from my Strogatz dynamics textbook. It feels like a good way to learn numerical ...
2
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3answers
164 views

Clustering with points lying along different 3D planes

I have a bunch of data points in 3D that lie along a few planes. What would be the best approaches to estimate the normals of these planes? Edit: There are roughly equal number of points lying along ...
2
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0answers
28 views

Piecewise-linear Continuations vs Marching Squares/Cubes

It seems that both piecewise-linear continuation and marching squares are methods to produce iso-contours of a scalar function given the function's values on a grid. It seems that piecwise-linear ...
2
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0answers
681 views

Discrete-time Algebraic Riccati Equation (DARE) solver in C++

I need to use a Discrete-time Algebraic Riccati Equation (DARE) solver for an embedded controller (with limited processing power) in a research project and sadly, I can't find any implementation of it ...
2
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0answers
57 views

Where does the seemingly official number of certain algorithms come from?

There are a lot of algorithms which seem to have been supplied an official number, such as Algorithm 76, Hierarchical clustering using the minimum spanning tree. Another example is Algorithm 123, ...
2
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0answers
61 views

Parallel compact schemes using the Parallal Diagonal Dominant (PDD) algorithm

I would like to use the PDD algorithm developed by Sun to solve tridiagonal matrices in parallel for the following compact finite difference scheme: $ \begin{align} \dfrac{1}{4}f^{'}_{i-1} + f^{'}_i +...
2
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0answers
60 views

Comparing the solutions to a multi-objective optimization problem

Suppose I have a multi-objective optimization problem, and I wish to find solutions using two different methods/algorithms. The result of each algorithms is a Pareto front. Comparing two different ...
2
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0answers
250 views

sum of n numbers with the power k

I am searching for a good algorithm to solve problem 487 on project-euler. I dont want code or something like that, I only want the name of the algorithm thats best suited. Till now I think of either ...
2
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0answers
101 views

Optimization based integration for MPM

I'm considering implementing (just for simplicity) the unconstrained implicit optimization based integration for Material Point Method as described in Chenfanfu Jiang's thesis on MPM (the minimization ...
2
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0answers
204 views

Solving a 3D (almost radial) convolution with FFT

I have a 3D integral that is almost a radial convolution of the form $$ \int d^{3}k'h(\mathbf{k'})g(|\mathbf{k-k'}|) $$ and I am looking for a fast and efficient algorithm (e.g. FFT) to solve it ...
2
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0answers
37 views

Finding errors in frequency from a Fast Fourier Transform from Gaussian fitting

I took a FFT of sound in a box generated by a frequency sweep over a range of frequencies, and have an array of frequencies and their corresponding FFT amplitudes. According to models for the ...
2
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0answers
52 views

SPECT reconstrction using MLEM

In Single-Photon Emission Computerized Tomography (SPECT) parallel beam reconstruction using Maximum-Likelihood Expectation–Maximization(MLEM), is it sufficient to scan the object around 180 degree? ...
2
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0answers
571 views

Exact line Search in Steepest descent

I wanted to clarify the idea of the exact line search in steepest descent method. An exact line search involves starting with a relatively large step size ($\alpha$) for movement along the search ...
2
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0answers
884 views

Divide and Conquer division algorithm explained (as used in GMP bignum)

I am trying to understand the divide and conquer division algorithm that is used in the GMP bignum arithmetic library. The code is very optimised and that makes it somewhat hard to understand. the ...
2
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0answers
119 views

Area of convex n-dimensional polytope

I am looking for an efficient algorithm to calculate the surface area of an irregular N-dimensional polytope. I have a description of this polytope both as coordinates of the vertices as as linear ...
2
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0answers
118 views

similarity/distance measurement between two ranked sequence

Is there an efficient way to measure similarity/distance between two sequences of ranked numbers/letters. The two sequences are of different length, and only have some elements in common? For example,...
2
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0answers
91 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 ...
2
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0answers
82 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 ...
2
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0answers
88 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 ...
2
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0answers
95 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 ...
2
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0answers
139 views

Algorithms for adding hydrogens on a molecule

I want to add hydrogens to some linear polymer molecules (polyethylenes). I know some working methods like using PyMOL internal function h_add. This method works, but hydrogens are added at distances ...
2
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0answers
99 views

Preconditioner for large size hermitian eigenvalue problems

Basically I try to compute several smallest eigenvalues of some sparse 50k*50k eigenvalue problems using matlab. $$Ax = \lambda Bx$$ With matlab eigs, it's not as fast as I expected. So I tried some ...
2
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0answers
189 views

Good approximate solutions for a MILP problem

The company I work for has been developing an application for real-time control of sewer networks. Every 5 minutes, a MILP problem is built or updated, then solved using Gurobi. For mid-sized cities, ...
2
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0answers
115 views

Algorithm to distribute symbols uniformly in a square grid?

Given a square grid of size $n\times n$ and $m$ symbols (say for example, alphabets A, B, C...), having $N(i)$ number of $i$th symbol; $\sum_{i=1}^{m}N(i) = n\times n$. Is there any computationally ...
2
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0answers
98 views

Estimating the maximum absolute value (magnitude) of the Laplacian for a given function?

As motivation, consider a function which is smooth and continuous but for some reason it is very expensive to perform routine calculations of finding the Laplacian on it (maybe because it is over a ...
1
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0answers
47 views

Assume $AX = C$. How to determine which entry of $BX - D$ is non-negative?

Let $A,B$ be $n \times n$ matrices and $C,D$ be $n \times 1$ matrices. Moreover, all entries of $A,B,C,D$ are non-negative. Assume that there is a unique matrix $X$ that solves $AX = C$. My goal is ...
1
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0answers
25 views

Newman algorithm yielding different result to what is given in his paper

Summary I am trying to implement Newman's algorithm for community detection, outlined in this paper. I am testing my implementation against one of the datasets used in that paper to benchmark the ...
1
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0answers
25 views

Unable to achieve semi-linear running time in computation of continuant

I am trying to compute the continuant of a list of numbers $a_0, a_1,...,a_n$, defined by the recursion relation: $K_{n+1} = a_{n+1} K_n + K_{n-1}$ and $K_0 = 1$ (see Wikipedia). I am trying to use ...
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0answers
18 views

SHREC 2010 Descriptors

I will appreciate if I may find someone how can clarify for me the part regarding the quality of feature descriptor, shown in the figure below: and this screenshot is from the article: SHREC All my ...