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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0answers
38 views

Jacobi method converging then diverging

I am working to solve Poisson's equation in 2D axisymmetric cylindrical coordinates using the Jacobi method. The $L^2$ norm decreases from $\sim 10^3$ on the first iteration (I have a really bad ...
1
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0answers
22 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 ...
1
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0answers
34 views

Manipulating/Extracting Data and Developing Methods - Language Choice [closed]

As a general programming enthusiast and aspiring Bioinformatician student I have an intermediate understanding of computing (languages) as well as Java, and to a lesser extent C++. Having knowledge in ...
1
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1answer
49 views

Algorithms for one-to-many assignment problem

I'm looking for a computationally efficient algorithm for solving the following type of assignment problem: I have two sets of points. Set A has N points and set B has M points. I'd like to establish ...
2
votes
1answer
133 views

Comparison of convex hulls [closed]

Consider a set of polytopes $P_i : i=1,2,...,k$ each of which has a structure as $P_i:= \{(x_{i1},x_{i2},..., x_{in})\; |\; x_{ij} \in [a_{ij}, b_{ij}] \subseteq [0,1]\}\;\; \text{for all}\;\; ...
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0answers
20 views

“Tunneling” optimization algorithm in Matlab

I was wondering if someone has implemented the "Tunneling algorithm" for the global minimization of a single variable function in Matlab. I am hoping to implement it on $[B, A - \lambda I]$. Where ...
1
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1answer
27 views

When we compute the complexity of a given algorithm related to image processing does the N refers to the number of Pixels in the image?

When we compute the complexity of an image processing algorithm, we get an $O(N)$. does the $N$ refers to the number of pixels in the image or to the height/width of the image, I mean it is computed ...
2
votes
2answers
114 views

C++ Library: What is the common libraries that do polynomial arithmetic?

I need to know what libraries (in C++) support polynomial arithmetic specially over a field. So I can give to it an array of coefficients of polynomial over a field and it returns the roots of ...
1
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1answer
67 views

Fast algorithms for computing only the generalized singular values (but not the vectors)

I am interested in computing only the generalized singular values, and was wondering if this was faster (and by how much?) than computing the full GSVD. In particular, I was wondering what the ...
0
votes
1answer
56 views

Is this the correct procedure for calculating matrix spectrum?

I am not sure if my question is on topic but I have a piece of Fortran code that is used to perform successive over relaxation. Prior to performing successive over relaxation the author is calculating ...
2
votes
1answer
35 views

Simple Path to Route Algorithm

I'm currently conducting research into subway paths, but stand in front of a problem, with no programming knowledge and an extremely short time-limit. Probably the question I am asking is trivial, ...
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2answers
91 views

Looking for a particular algorithm for numerical integration

Consider the following differential equation \begin{equation} p(t) = \frac{\partial q(t)}{\partial t} \end{equation} where $t \in (0,\infty)$. I have a build a code that spits out values of the ...
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0answers
82 views

General algorithm to solve systems of symbolic equations

I want to simplify (solve) a system of linear + nonlinear symbolic equations as much as possible. the equations are of random orders, without differentiation. is there a general & well-known ...
1
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2answers
129 views

Ideas on how to search nearby geospatial data fast

I am looking at a very simple problem, but can't quite find the best solution. I need to accept a lat/lon coordinate and based on that coordinate find all the points within roughly ~1km (accuracy is ...
9
votes
2answers
171 views

How does weak convergence feel, numerically?

Consider, you have a problem in an infinite dimensional Hilbert or Banach space (think of a PDE or an optimization problem in such a space) and you have an algorithm that converges weakly to a ...
2
votes
1answer
60 views

Does this “reverse binary search” have a name?

Normally when searching in sorted sets, binary searches are a fast, nice and easy way to locate data. It does however break down in the hypothetical scenario of having a set of arbitrarily large but ...
-1
votes
1answer
65 views

Is iteration an efficient algorithm in this case? [closed]

My task in numerical analysis is We are interested in finding values of β0 for which z(x) = 2500. Use an efficient algorithm to determine the rays which pass through the receiver. Now I'm ...
2
votes
1answer
34 views

website for algorithm analysis in various languages

Not sure if this is the right place to post this, but some time ago i stumbled upon a website which had algorithms submitted by users in different languages... I am unalbe to find that website, anyone ...
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0answers
54 views

Bijection between polyhedrals

Does there exist a bijection between a general axis-parallel polytope in $\mathbb{R}^n$ and a polytope embedded in a unit hypercube in $\mathbb{R}^n$? This means that the bijection must preserve the ...
1
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1answer
25 views

extract exhaustive mutually exclusive intervals from larger set of intervals [closed]

I have a collection of time intervals with integer valued endpoints , e.g. (1,2), (2, 6) (5,6), and the number of events falling in each time interval, and I would like to determine if from them I ...
1
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0answers
12 views

Enumerating set combinations in an order that maximises the number of previously unseen subsets

Consider a set $S=\{a,b,c,d,e,f,g,h,i,j,k\}$, $\left|S\right|=11$. There are ${11 \choose 5} = 462$ combinations of $S$'s members of size $5$. There are $462! \approx 1.419 × 10^{1032}$ possible ...
1
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3answers
73 views

Should a randomly-seeded genetic algorithm give deterministic optimized solutions on each run?

I am going to rewrite an algorithm using genetic methods for mutating my solutions, and I am wondering what I should expect and only consider my algorithm "optimized" or "finished" if various runs of ...
0
votes
1answer
186 views

What is the fastest algorithm for computing the inverse matrix and its determinant for positive definite symmetric matrices?

Given a positive definite symmetric matrix, what is the fastest algorithm for computing the inverse matrix and its determinant? For problems I am interested in, the matrix dimension is 30 or less. ...
1
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2answers
100 views

Determining if samples fit a 3D Gaussian distribution

I have a collection of sample particles, with (x,y,z) coordinates generated by a simplified Monte Carlo-like code. I expect that these particles will follow an anisotropic diffusion process, which ...
0
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0answers
33 views

Optimization of nonlocal stencil-like operator on subset of regular grid

I am trying to optimize the execution time for this particular piece of fortran code. Details: i_gc is a (ngpts, 3) array of containing (i,j,k) indices for each grid point. This is a subset of the ...
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0answers
27 views

Percentage based weight ditribution

I have a say 3 different algorithm which gives a total weight value for individual algorithm. I would like to give weights for each algorithm. Currently I am using e.g. Algorithm 1 - 8 elements - sum ...
1
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0answers
23 views

Minimum effort merging of two sets

I have the following problem. I have two sequences of elements $A = [a_1,a_2,\cdots,a_n]$ and $B = [b_1,b_2,\cdots,b_m]$. I can build a matrix $D[n \times m]$ where $d_{ij} = d(a_i,b_j)$ My greedy ...
0
votes
1answer
65 views

Is there general algorithms to solve such 3D cutting problems?

Suppose a cuboid $\mathbb{A}$ has $L$,$M$ and $N$ as its length, width and height respectively, where $L\ge{M}\ge{N}>0$; Now we want to cut $\mathbb{A}$ into smaller cuboids with length $x$, width ...
3
votes
1answer
103 views

What is the case of trade-off in different Runge Kutta methods

There are so many Runge Kutta methods, including Dormand-Prince 45 Cash-Karp 54 Fehlberge 78 Is there any comparison between them? What is each approach sacrificing? What is the general ...
2
votes
2answers
122 views

Calculate contour line length

I would like to know the algorithm to calculate contour line length. Suppose we have numerical data set of an function $f(x,y)$. How could I calculate the length of the line from $(x_1,y_1)$ to ...
1
vote
1answer
81 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
votes
0answers
50 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 ...
0
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0answers
25 views

Genetic Algorithm in linear cut optimization with reuse

As stated in the title i have a problem of linear cut optimization that i need to solve with a genetic algorithm. No problem if i have all the possible pieces to cut that are stically defined when ...
3
votes
2answers
876 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 ...
6
votes
1answer
113 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
votes
3answers
237 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 ...
0
votes
0answers
29 views

Find out the expression for angular speed in terms of time

The orbit of a small mass orbiting to a much larger mass (e.g. a small planet relative to a fixed star) is described by $$ u=\dfrac{1+e\cos{\theta}}{l} $$ where $u = 1/r$, $r$ and $\theta$ are the ...
1
vote
3answers
209 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? ...
0
votes
1answer
29 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 ...
1
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0answers
23 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 ...
0
votes
0answers
20 views

An algorithm to produce, not necessarily efficiently, another algorithm that efficiently solves the Rubik cube

How complex is the task to formulate an algorithm that produces, not necessarily efficiently, another algorithm to efficiently solves the Rubik cube? Has it been attempted before? What is the latest ...
1
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0answers
86 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 ...
0
votes
0answers
71 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 ...
2
votes
0answers
64 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
votes
1answer
89 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 ...
1
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3answers
151 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 ...
7
votes
1answer
173 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 ...
2
votes
0answers
44 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 ...
3
votes
3answers
152 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
votes
1answer
72 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 ...