# All Questions

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### Am I using cyclic reduction to parallelize this algorithm?

I am attempting to implement a modified anisotropic-diffusion filter on the GPU. The methodology I describe here including the equations and code listing are taken from this paper . The author of ...
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### 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, ...
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### 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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### Direct or iterative solver for ill-conditioned problems

I have to solve an ill-conditioned sparse matrix. Once I read that iterative solver are the better tool for such problems. Is that true? If yes, why?
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### Finding self-kissing points on a plane curve?

I have a curve in the complex plane given by $$f(t) = \sum_k r_k\exp(2\pi\mathrm{i}(t+\varphi_k)p_k).$$ Some of the parameters are specially chosen: $r_k>0$, $\sum_k r_k=1$, $p_k\in\mathbb{Z}$, ...
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### Problem solving on GPU / FPGA

I was just reading this paper (http://math.ipm.ac.ir/~tayfeh-r/papersandpreprints/h428.pdf) in it some algorithm found a solution to a problem within 12 hours on a cluster of sixteen 2.6 GHz PC. I was ...
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### Help with the definition of constraints for a joint optimization problem

A trajectory is piecewise defined by the following polynomial form: $$f(t) = a + bt+ct^{2}+dt^{3}+et^{4}+ft^{5}+gt^{6}+ht^{7}+it^{8}+jt^{9}$$ for every single segment composing the trajectory (the ...
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### GAMS solvers: which one to use

The other day I had a discussion with a friend about the GAMS solvers and we were wondering what are the mathematical differences between the solvers. Which one to use for which kind of problem? How ...
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### Is it possble to store a counter that could reach $\lfloor \frac{N}{x}\rfloor$ using $\lceil\log_2(N+1)\rceil$ - $\lfloor\log_2 x\rfloor$ bits? [on hold]

Let $x,N$ be positive integers. I'd like to store a counter which could reach value of $\lfloor \frac{N}{x}\rfloor$ (i.e. could take any value in $0,1,\ldots,\frac{N}{x}$) using ...
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### Value of density when there are no or very few neighbours in SPH simulation

Sorry for the noob question. I am trying to implement SPH using the directions shown in this paper. The density needs to be updated using the formula The smoothing kernel is If there are no ...
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### Manufactured solution for pressure based 3d incompressible Navier-Stokes solver with wall boundaries

I already successfully verified my solver (SIMPLE-type FVM-method) with the following manufactured solution (3d Taylor-Green vortex) on the solution domain $[-1,1]^3$ with Dirichlet boundary ...
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### Find $\min x^TAy$ subject to $1^Tx=1^Ty=1,x\ge 0,y\ge 0$

In the following problem, $A$ is a given $\mathbb{R}^{m\times n}$ matrix: \begin{align} \mbox{minimize}\quad & x^TAy \\ \mbox{subject to}\quad & 1^Tx=1^Ty=1, \\ & x\ge 0,y\ge 0. ...
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### Shared memory parallel computing solutions compared

As of 2015, what shared memory parallel computing solutions are available? What are the advantages and disadvantages of each for various use cases arising in high performance scientific computing? I ...
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### What are the novel MOOP method?

As you know, the multi-objective optimization methods are developing so fast, i.e.,epsilon constraints. I have a problem that I want to apply the most recent MOOP method for it. Please tell me the ...
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Basically I have the following equation of motion, for some wave packet $\mathcal{Q}(z,t)$: $$\partial_t \mathcal{Q}(z,t) = f(z)\mathcal{Q}(z,t) + \int_{-\infty}^{\infty}\text{d} z' ... 0answers 30 views ### Library for calculating determinants with Kronecker products I need to calculate a determinant consisting of vectors, using the Kronecker product as product. As an example I would need to be able to calculate: \left| \begin{array}{cc} ... 0answers 26 views ### Elasticseach is not matching ”_id” between the clusters [on hold] I have two Web Servers ws001 and ws002 working as load balance for Elasticseach and I am trying to catch/count the hits for a specific page which is something like this: mysite.com/listing/item-123/. ... 0answers 15 views ### Is there a standard for determining the accuracy of a polygon interpolation technique? I'm looking into polygon interpolation, and was curious if there are any standards for determining the accuracy of polygon interpolation techniques. I've been looking through papers and lecturers ... 0answers 44 views ### Programming language for scientific computation [duplicate] What programming language is best to learn for scientific computation? Fortran, C, Python? 0answers 40 views ### Laplacian discretization for parametric curves I know how to compute the discrete Laplacian of a graph and of a mesh (the Laplace-Beltrami operator). Is there an analogous definition for the computation of the Laplacian of a parametric curve ? ... 1answer 59 views ### Visually appealing ways to plot singular vector fields with matplotlib or other foss tools What is the best way to get a visual appealing plot of a singular vector field (if you want to visualize also the field strength). As an example I am playing with the electric fields of two point ... 0answers 23 views ### How to speed up calls to integral2 in matlab I am performing a 2D integral for each time step of a calculation. The problem is that I need to vary through all possible permutations of a1,a2 (which always ... 1answer 52 views ### Simple way to derive transpose of a vectorized operation In a program I'm writing, I have a sub-routine that does some vectorized linear operations (specifically differentiation). Say for convenience I have defined the following inline function, which ... 0answers 18 views ### Compare Sumatra and Biolite I want a tool that can handle handle data provenance and record the following: Tools version State of machine-Linux,Java version Node PBS id,time stamp, who command I was reading about Biolite and ... 2answers 86 views ### How to impose boundary conditions on eigenfunction problems? I am trying to solve for the eigenfunctions of a (1D) differential operator using finite differences:$$A \, f(x) = \lambda f(x)$$Here is an example in Python where A = \partial_x^4: ... 0answers 35 views ### How to determine the minimum number of multiplication needed for a specific expression? Is there any algorithm to determine the minimum number of multiplication(division) of a specific expression? and the optimal expression form for implementation? For example, given values of ... 1answer 57 views ### Discontinuous Galerkin, residual orthogonal to test functions? I am a little confused about where does the mass and stiff matrix come from. In Discontinuous Galerkin we divide the domain in elements, \Omega = \cup^K_{k=1} D^k. Then assume the solution u can ... 1answer 42 views ### Modified diffusion equation and unstabilities I am trying to simulate the phase separation of a binary mixture. If the free energy F is known as a function of the concentration c, the dynamical equation is:  \frac{\partial c(x,t)}{\partial ... 1answer 50 views ### Is it possible to eliminate the inner sum to evaluate numerically? Any hints on how to simplify the following double sum to be able to find the sum at least numerically?$$\sum_{n=2}^{\infty}\frac1{n(n^2-1)} \sum_{k=1}^\infty \frac{(k-1/n)^{2n-2}}{(k+1/n)^{2n+2}}$$... 2answers 56 views ### Computation of multipole expansion of potential not converging According to Beatson and Greengard's short course on FMM: ( Eq. 5.15 & 5.16 setting k=1, q=1 ) We can approximate a potential \phi = 1/(r-R) using:$$ {1\over |\vec{r}-\vec{R}|} = ...
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From the order condition $$\sigma(w)=\frac{\rho(w)}{\ln w}+O(|w-1|^p)$$ I get $$\sigma(w)=1+\frac{3}{2}(w-1)+\frac{5}{12}(w-1)^2=-\frac{1}{12}+\frac{2}{3}w+\frac{5}{12}w^2$$ Those coefficients are ...
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### Convergence of a DASPK depending on DAE formulation

I have a system of non-linear DAE and I noticed that the system does not converge if some of the equations are not differentiated. For example, if the control volume equation is represented as this: ...
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### 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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### 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 ...
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### quick projection

I am using level method to solve non-smooth convex programming problem (where the objective function is given by an oracle from another program ): http://www2.isye.gatech.edu/~nemirovs/Lect_EMCO.pdf ...
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### Converting quadratic constraint to linear matrix inequality

So I have the quadratic programming problem: (x is the variable) $$\text{Minimize}\;\; x^T\Sigma x$$ $$\hspace{15mm}\text{Subject to}\;\; p^Tx = \frac{1}{n}p^T\boldsymbol{1}$$ ...
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### Python: Boundary constraint issue with Scipy.optimize

It seems that I have an issue with my boundary conditions when I use the function [fmin_l_bfgs_b][1]. ...