Questions tagged [algorithms]
A description of the specific steps needed to solve a particular problem in an unambiguous way, expressed in an abstract form.
500
questions
2
votes
3answers
181 views
On the reordering of sparse matrices
I have been reading on different techniques used to reorder sparse matrices to achieve better performance, the most popular being the Cuthill-McKee or Reverse Cuthill-McKee algorithm. Most of those ...
2
votes
0answers
75 views
Computing Singular Value Decomposition of small ($4\times 4$) matrices
I need to compute the Singular Value Decomposition (SVD) of many $4 \times 4$ matrices. I'm looking for SVD algorithms specialized for small matrices. I've read that the ...
5
votes
1answer
280 views
Cheap recalculation of eigenvalues and eigenvectors for a low-rank update of the matrix
Suppose I have a correlation matrix, $A$, and I already have the eigenvalues and eigenvectors of this matrix.
For a given vector, $\mathbf{\mathit{v}}$, I want to calculate the eigenvalues and ...
-1
votes
0answers
51 views
Cost/Complexity involved in solving a Linear system by Gaussian Elimination
What is the cost of solving a linear system over a field F of size q by Gaussian Elimination?
Thanks!
0
votes
0answers
21 views
Producing Voronoi diagram in three dimensional
A Voronoi diagram is a kind of tesselation that divided the medium into polygons in 2D and polyhedrons in 3D.
Although there are many algorithms to construct a Voronoi diagram, some of them are faster ...
3
votes
3answers
97 views
What are some algorithms to calculate the width of an arbitrary polygon when a bounding box approximation is inaccurate
What are some alternative algorithms to creating a bounding box for finding the max width of a concave, simple winding polygon, like the one in the below image? I prefer solutions that are more ...
0
votes
0answers
65 views
Derivative-free ill-conditioned non-linear least squares
I am looking for a package which can solve (non-linear) least squares problems without the use of derivatives (because of an expensive model), but which also deals with ill-conditioning well (such as ...
0
votes
0answers
39 views
Explanation of Givens rotation in Jacobi Rotation SVD
I'm trying to implement Singular Value Decomposition (homework of sorts) via the Jacobi Rotation method (more info here, pages 11 and 12).
I am stuck at the bullet saying (sorry for the picture, but I'...
2
votes
1answer
35 views
How do you construct a self-similar binary structured-tree?
Please excuse me if this question somehow looks trivial or not really interesting, but I recently have a hard time to convince someone else that my algorithm for constructing a self-similar binary ...
0
votes
0answers
20 views
Hawkes Process : recursive formula for : $R'_{m,n} (k) = \sum_{ \{i : t_i^n < t_k^m \} } (t_k^m - t_i^n) \exp ( - \beta_{m,n} ( t_k^m - t_i^n ) ) $
Following the advice of a fellow mathematician, I am asking my question here from (https://mathoverflow.net/questions/365554/hawkes-process-recursive-formula-for-r-m-n-k-sum-i-t-in-t)
I need to use a ...
0
votes
0answers
44 views
Surface mesh from labeled 3D points
I'm trying to figure out how to create a surface mesh from a set of labeled 3D points. The 3D object could be something like part of a cave system or asteroid where there would be parts of the surface ...
1
vote
0answers
22 views
Combining many probabilities, modifying, seeking general formula
CONTEXT
I need to combine the probability of occurrence of many thousands of events for millions of individuals (trees) in an agent-based/individual-based simulation model developed in NetLogo (agent-...
2
votes
1answer
37 views
Question regarding the energy computation of the Ising-Spin Model
In most of the Monte-Carlo-Algorithms I studied, I found, at the place where they compute the energy, always a line of code, where they divided by four.
For example, this code-snippet is taken from ...
1
vote
1answer
95 views
Machine Learning for Optimization
I have a function which takes 100+ coefficients and outputs $x$. I wish to optimise $x$.
Running the simulation 50 000 times will take around 15 minutes, however, this happens in parallel - and the ...
1
vote
0answers
50 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 ...
0
votes
2answers
65 views
Best way to find biggest & smallest number in a random list?
Given a list of some length, containing random numbers.
What method would need the least amount of checks to find the largest & smallest number in the list?
My best guess is: (list_length)/2 ...
-1
votes
1answer
28 views
An almost surly fine-time game of coin toss where you win with probability $p$
Given a fair coin and a number $p\in(0,1)$. How do you design a game that finishes in a finite number of tosses with a probability of $1$? And further, with the probability $p$ you win the game.
I ...
0
votes
0answers
35 views
What constraints, if any, are there on constructible patterns in Conway's Game of Life?
Conway's Game of Life is Turing-complete.
Interesting demos of this:
A clock
Tetris
I note that Turing-completeness doesn't require that any specifically encoded state be reachable, does it? ...
1
vote
1answer
50 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 ...
2
votes
2answers
98 views
Using MILP to place a set of primers along a genome
Define variables $p_i,u_i\in\{0,1\}^G$, for $i=1,\ldots,8$ and $G=30000$.
Let $v$ be a constant vector also in $\{0,1\}^G$, with approximately 25% of its entries equal to $1$ (randomly located).
Let ...
1
vote
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 ...
0
votes
0answers
23 views
Boundary conditions for triangular lattice in comsol
I am trying to simulate an infinite 2D triangular lattice in Comsol but I am confused that how should I use periodic floquet boundary conditions on the unit-cell.
A unit cell that I am using is given ...
3
votes
1answer
85 views
Can you compare integer part of two fractions without division?
Suppose we need to compare
$\left \lfloor{a / b}\right \rfloor $
and
$\left \lfloor{c / d}\right \rfloor $
.
One way would of course be to calculate $a/b$ and $c/d$ by division. Is their a faster way?
5
votes
2answers
142 views
Fast algorithm for computing the similarity between two arrays
Suppose there are two arrays (They have the same length), I want to give a quantitative description about the similarity between them. I define a formula like this, which means we can shuffle them ...
5
votes
1answer
60 views
Is there an efficient algorithm for calculation of continued fraction expansion from decimal digits?
Suppose to calculate the continued fraction expansion of $\pi$, the common-sense algorithm would be to take the decimal part, perform inversion, which will give the next term as integer part, and the ...
7
votes
1answer
120 views
Numerically stable and fast sum of last K elements in sequence
Suppose I have a long, possibly infinite, sequence $x := [x_1, x_2, ...]$, and I want to use it to compute another sequence $y:=[y_1, y_2, ...]$ where each element is the sum of the last K elements of ...
5
votes
0answers
73 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 ...
2
votes
0answers
29 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
votes
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 ...
1
vote
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 ...
3
votes
1answer
70 views
Evaluate 3D Shape Descriptor
I'm trying to create my own 3d shape descriptor, the idea is that how I may evaluate how much my descriptor is well and good?
What I checked is that they evaluate descriptors through shape matching, ...
3
votes
0answers
68 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^{\...
10
votes
3answers
343 views
Should benchmarkings be done at all? What is the point?
I am reading a paper which compares algorithm A versus algorithm B.
It shows that algorithm A is faster than algorithm B via benchmarking that shows the CPU time.
What is the point of this? Any ...
1
vote
0answers
69 views
How to approach geographic data interpolation by distance?
let's say I have a set of geographic locations (lat, lng) resulting from a query. Those locations have some kind of internal ranking, my set is sorted by this number in a descending order.
Now I'm ...
3
votes
1answer
85 views
Calculate Transformation Matrix between two sensors
My question is if I can calculate the transformation matrix between two sensors.
Each sensor provides a $4\times 4$ matrix for every timestep recorded.
The sensors are moving and have some noise in ...
0
votes
0answers
70 views
What is Voronoi particle tracking?
I've been trying to track this down, but google is giving paywall papers that don't appear to be directly related to computational science, or simply don't explain the source algorithm.
There's an ...
5
votes
1answer
268 views
Understanding butcher tableau when it comes to implicit methods
I've been learning about butcher tables and am having some difficulty understanding how to translate them when it comes to implicit methods. Specifically, I'm looking at backwards Euler:
\begin{array}...
2
votes
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 ...
1
vote
0answers
58 views
Hybrid Ellpack-Itpack (ELL) + COO Sparse Matrix Representation decomposition threshold
Hybrid ELL-COO sparse matrix representation can be done as in the picture, I was looking intensively, however I couldn't find out what is the threshold of decomposing the original matrix into ELL part ...
3
votes
1answer
83 views
Efficient computation of leading eigenvector of a matrix product of the form $ADA^T$, where $D$ is diagonal
Let $A=[A_1|\ldots|A_m] \in \mathbb R^{n \times m}$ with $n \gg m \gg 1$ and $D=\text{diag}(d_1,\ldots,d_m)$ where $d_1,\ldots,d_m > 0$, and consider the $n\times n$ positive-definite matrix $X=\...
0
votes
0answers
32 views
solving electron motion in undulator by Boris method
I am trying to use Boris scheme to solve the electron trajectory in undulator.
The undulator field I used is:
$$B_x = b_0\sin(2\pi \tfrac{z}{\lambda_u})$$
where $b_0 = \dfrac{2\pi c_{0}K}{q m_{e} \...
1
vote
1answer
172 views
Weighted moving variance
i have a time-series and, in analogy with exponentially weighted moving average, i would like to compute the exponentially weighted moving standard deviation or variance in an efficient, numerically ...
0
votes
1answer
65 views
Dealing neighbor list in NVT Monte Carlo (MC) simulation
I'm making a NVT Monte Carlo (MC) simulation code with only short range interaction.
I found many MC tutorial codes (usually Lennard-Jones system) in online. However, most of them are doing energy ...
4
votes
2answers
144 views
Efficient algorithm to decide if a graph is a cactus?
A cactus is a connected graph in which every edge belongs to at most one simple cycle.
How should one modify the Depth First Search algorithm to obtain an efficient algorithm that determines if a ...
4
votes
1answer
228 views
Fast algorithm for computing cofactor matrix
I wonder if there is a fast algorithm, say ($\mathcal O(n^3)$) for computing the cofactor matrix (or conjugate matrix) of an $N\times N$ square matrix. And yes, one could first compute its determinant ...
1
vote
1answer
37 views
How is the D value being updated at simple RRT algorithm?
I am studying the following lecture (image) regarding 5 iterations of the simple RRT algorithm.
I am trying to understand how each value is being updated regarding each iteration. I have figured out ...
0
votes
0answers
33 views
A preconditioner for self-consistent iteration
I tried to derive a preconditioner for self-consistent iteration similar
to section IX in arXiv:0804.2583.
For simplicity, consider here only
one orbital (one or two electrons) systems.
Suppose that ...
0
votes
1answer
268 views
Chip testing problem
An engineer has n supposedly identical integrated-circuit chips that in principle are capable of testing each other. The engineer test jig
accommodates two chips at a time. When the jig is loaded, ...
4
votes
1answer
46 views
Single-variable multimodal derivative-free optimization (for a well-behaved function)
Are there well-established approaches to single-variable multimodal optimization?
Given $f:\mathbb{R}\rightarrow\mathbb{R}$ that:
has several local minima within a given range of interest $[a,b]$
is ...
3
votes
1answer
112 views
How to justify using available code (in different language) for comparing algorithms
I have proposed an algorithm for a scheduling problem in a submitting paper. In the revision, the reviewer asked us to compare with another algorithm from the literature. Our algorithm is in MATLAB, ...
