# Questions tagged [algorithms]

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

447 questions
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### Comparison between CashKarp Method and Dormand Prince Method - Runge Kutta Method

Can Cash Karp Method be used for integrating a nonsmooth solution ?. Because Dormand Prince method gives an error while integrating nonsmooth solution How can nonsmooth function can be integrated? I ...
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### Literature on comparing Simplex and Interior-Point-Methods (or combining both of them)

Do you know some interesting literature concerning the comparison of Simplex and Interior-Point-Methods referring to linear optimization? I also read about the possibility of combining both of them ...
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### What are the prominent algorithms for solving systems of linear inequalities?

Why, you may ask? The Python sympy symbolic library provides solutions to single, linear Diophantine equations in terms of parametric variables. For instance, ...
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### Min supporting line for a set of points

I'm trying to solve exercises of the book "Computational Geometry in C" by O'Rourke. Could you please help me with this one? Design an algorithm to find a line $L$ that: has all the points ...
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### comparison of CPU time and normalization

How to normalize the CPU time for comparing algorithm execution time on systems with different hardware configurations?
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### Simple finite volume method for compressible Navier-Stokes equations

I am interested in writing a simple, cell-centered, 2D FVM code for the unsteady, compressible Navier-Stokes equations (including shocks). Most of my experience is with finite difference and finite ...
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### Chinese character component-based layout engine algorithms [closed]

I am looking for a PDF describing Chinese character component-based layout engine algorithms. These should allow for recursive encodings of radical and non-radical components, and the encodings should ...
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### Performing computations over the set of constructable numbers

The set of constructable numbers is commonly defined in one of two ways: the set of finite numbers reachable from the rational numbers through a finite sequence of addition/subtraction, ...
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### What is a good algorithm, and framework, to calculate centres of gravity or mass (cog)?

I'd like to take an photograph, subdivide it into a tesselation, either of squares, or (ideally), hexagons, and then find the centre of gravity (or, if you prefer, centre of mass) of each cell of the ...
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### Iterative root finding of 2-dimensional system of non-linear equations with monotonicity properties

Let $f(x,y)$ and $g(x,y)$ be two $\mathbb{R}^2\rightarrow\mathbb{R}$ functions, both strictly increasing in both arguments. Assume that they are well-behaved functions (continuous, differentiable, etc....
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### Defining a pixel neighborhood in an array in MATLAB

I am working with matrix operations in MATLAB, and I would have the following problem. I have matrix containing zero elements: a=zeros(100,100) and another ...
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### Applying the result of Cuthill-McKee in SciPy

I have applied SciPy's implementation of the Cuthill-McKee algorithm to a $48 \times 48$ sparse non-symmetric matrix in Compressed Sparse Row (CSR) format and the output is an array of length $48$ ...
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### Efficiently computing the properties of a Chebyshev series

Suppose we have some function $f(x)$ defined as a Chebyshev series up to order $M$: $$f(x) = \sum_{n=0}^{M} c_n T_n(x).$$ For a given coefficients vector $\mathbf{c}$, and $x \in [-1,1]$ I'm ...
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### Find alternative path closest to original

I have a set of points in a 2D space. I want to connect the outer points so I get the convex hull. The problem here is that there is a limit to the distance between two points. Let me clarify that ...
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### Formation sketching; trouble with sampling unit optimization

I'm looking for assistance in understanding a concise portion of a paper that involves a quadratic equation, so that I can properly implement it. There are 2 versions of the paper. Each paper ...
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### 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 ...
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### 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 ...
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### Nearest Neighbors in radius via Z-order order curve?

Given a $M\times M\times M$ 3D cube grid $C$, how can I map the 3D grid-coordinates to 1D coordinates such that every cell's nearest neighbors can be represented by a continuous range of corresponding ...
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### What is meant by “operations”?

In this paper, on page 243, we have $$d_{jk} = \frac{a_j}{a_k(x_j - x_k)}$$ where $$a_k = \prod_{l = 0;l\neq k}^{N}(x_k-x_l)$$ Now, $a_k$ requires evaluating N multiplications. Why does the author ...
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### Markov (Chain) image generators?

Markov Chains can be used to generate, or auto-complete, text. https://en.wikipedia.org/wiki/Markov_chain#Markov_text_generators Training text is read, and some information about the text is ...
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### Help understanding and implementing fast multipole method for N-body

I've been trying to understand the Fast Multipole Method but not really getting anywhere. It seems like the fastest mainstream N-body simulation algorithm, and I would like to implement it in an ...
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### N-body simulation optimisation, looking for name or existing work

during the development of my N-body simulation with visualisation in WebGL, I devised an optimisation, and I'm wondering if it has a name. I find it unlikely that it has never been done before. It ...
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### I need to deconvolve the image of a fluorescent bead without the Point Spread Function in MATLAB

I am aware that I could use deconvolution algorithms such as LUCY, Weiner and Blind but I am confused as to how to estimate the PSF (point spread function), which is needed for the LUCY and Weiner ...
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### Round-robin pairings: Everybody need to meet everybody

I have the following problem, I have a class of N people and I want them to do stuff by pair, but I want them to do this with everybody but as fast as possible. For N = 4 I got this: ...