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11
votes
2answers
7k views

CVXOPT VS. OpenOpt

CVXOPT: http://abel.ee.ucla.edu/cvxopt/index.html OpenOpt: http://openopt.org/Welcome What's the relation between them? What are the advantages/disadvantages of them, respectively? BTW, is there any ...
0
votes
3answers
181 views

Equivalence of linear systems, solving one instead of the other

This question is related to recently posted one, but I guess it deserves a separate attention. Suppose a symmetric matrix $L\in\mathbb{R}^{n\times n}$ is given, and a rectangular matrix $A\in\mathbb{...
14
votes
1answer
278 views

How do low rank modifications affect Krylov method convergence?

Say I have a linear system $A x = b$, which converges quickly using a suitable Krylov method (such as CG or GMRES) for all $b$. If $B$ is a matrix with low rank $r$, will the same Krylov method on ...
2
votes
3answers
9k views

Dealing with non-monotonically increasing data

How do you deal with data that you need to be monotonically increasing in order to work with interpolation libs and other functions, when it is in fact not monotonically increasing?
3
votes
1answer
232 views

Looking for parMetis visualizer?

Is there any visualizer for parMetis (mpmetis), which can visualize FEM mesh grids after partitioning?
1
vote
0answers
497 views

How to solve advection equation using semi-lagrangian method?

I am working on something that involves solving an advection equation $\partial{x}/\partial{t}+\vec{u}\cdot\nabla{x}=0$ in 3D. I discretized the space into 3d cartesian grid and used the Semi-...
8
votes
2answers
7k views

Simultaneous maximization of two functions without available derivatives

I have two variables k and t as functions of two other variables p1 and ...
3
votes
1answer
349 views

Parallelization of LSE solvers using CUDA

I want to know methods which are fully parallelizable on CUDA architecture. I have implemented the Jacobi and Conjugate Gradient methods and now Im thinking about the Bi-Conjugate gradient method. I ...
25
votes
6answers
7k views

Visualizing very large link graphs

I am looking for a tool to visualize very large directional link graphs. I currently have ~2million nodes with ~10million edges. I have tried a few different things, but most take hours to even do ...
8
votes
0answers
438 views

What's a good numerical/optimization software package for solving the 2-D optimal stopping problem?

I am looking for a numerical software package to help me solve the 2-dimensional "free boundary" PDEs that arise in optimal stopping problems. In one dimension a standard optimal stopping problem in ...
3
votes
1answer
140 views

How to add perturbation to a base state in physical grid space?

For study 3D instabilities problem i.e a base state (velocity field and temperature field) and an additional perturbation. The method must be independent of the type of instabilities considered but ...
8
votes
1answer
2k views

Open-source, thread-safe implementation of convex optimization solvers in C/C++?

Is there an open-source, thread-safe implementation of convex optimization solvers in C/C++? Some libraries such as NLopt, Ipopt, OPT++ don't meet my requirements. OPT++ and Ipopt aren't thread-safe,...
2
votes
1answer
187 views

Recovering coordinates by eigendecomposition without double-centering

Suppose an Euclidean distance $D\in\mathbb{R}^{n\times n}$ matrix between a set of $n$ objects is given. To obtain inner-products (which will be further be used to recover coordinates), entries of $D$ ...
8
votes
2answers
407 views

Octree cubes to tetrahedrons

I'm trying to learn more about volume meshing and have decided to try to implement a simple volume mesher. The strategy I have chosen is to subdivide my space using an octree, refined based on some ...
6
votes
1answer
11k views

Concave polygon 'hull' finding

I implemented an algorithm to find the alpha shape of a set of points. The alpha shape is a concave hull for a set of points, whose shape depends on a parameter alpha deciding which points make up the ...
6
votes
1answer
1k views

Appropriate space for weak solutions to an elliptical pde with mixed inhomogeneous boundary conditions

I'm working with the following mixed inhomogeneous boundary value problem: $\nabla(\kappa\nabla u)=f$ in $\Omega$ with $\partial\Omega = \Omega_1 \bigcup\Omega_2$ such that $u=g$ on $\partial\...
2
votes
2answers
316 views

Numerical solution of fractional integro-diffrential equ. using collocation method?

problem comes from "Numerical solution of fractional integro-differential , equations by collocation method , E.A. Rawashdeh, Department of Mathematics, Yarmouk University, Irbid 21110, Jordan" $D^...
1
vote
1answer
87 views

neural networks: multilayer on-off perceptrons

This article says that all any multilayer perceptron with a linear on-off functions for all the neurons can be reduced to a two-layered perceptron. Now, consider a two input/one output perceptron. ...
15
votes
3answers
1k views

Numerical methods for discontinuous r.s. ODEs

what are state of art methods for numerical solution of ODEs with discontinuous right side? I'm mostly interested piecewise-smooth right side functions, e.g. sign. I'm trying to solve the equation of ...
2
votes
1answer
157 views

FEM simulation of a material being stretched

I'm trying to teach myself FEM. The problem I have in mind is to completely investigate a plastic (e.g rubber band) being stretched (therefore, boundary conditions move as you stretch). I imagine this ...
3
votes
2answers
106 views

How can you explain the following bound on the inner product?

I am reading a paper on stability of CG, and I came across the following statement: \begin{equation} \frac{\|A\|\,\|p\|^2}{\langle p,Ap\rangle} \leq \kappa(A) \end{equation} where $\kappa(\cdot)$ is ...
1
vote
1answer
54 views

Finding most informative feature subsets given dataset, clustering algorithm and gold standard partition

I have an $n \times m$ matrix of data $\mathbf{D}$ as well as a $k$-partition $P$ of $n$ indices each representing a row in a dataset. Assuming an arbitrary clustering algorithm $A$, I would like to ...
10
votes
2answers
385 views

Task-based shared-memory parallel libraries in Scientific Computing

In recent years, several libraries/software projects have appeared that offer some form or another of general-purpose data-driven shared-memory parallelism. The main idea is that instead of writing ...
1
vote
2answers
2k views

Gram-Schmidt method to identify linearly dependent vectors

A method to orthogonalize a set of vectors (vectors of unit length that are mutually orthogonal) is the Gram-Schmidt process: http://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process Note that the ...
12
votes
1answer
7k views

Understanding the Wolfe Conditions for an Inexact line search

According to Nocedal & Wright's Book Numerical Optimization (2006), the Wolfe's conditions for an inexact line search are, for a descent direction $p$, Sufficient Decrease: $f(x+\alpha p)\le f(x)+...
1
vote
1answer
120 views

Adaptive Linear Algebra Libraries

After reading the first answer here about how the best way to find the most performant sparse solver is to try almost everything, I began to wonder if there was any past work on libraries or research ...
2
votes
3answers
940 views

Convergence of the gradient descent and linear vs non-linear fixed point iteration

Suppose a system $$Ax=b$$ is given, with $A\in\mathbb{R}^{n\times n}$ being a symmetric positive-definite matrix, and some non-zero $b\in\mathbb{R}^n$. The gradient method with optimum step length can ...
33
votes
3answers
14k views

How to choose a method for solving linear equations

To my knowledge, there are 4 ways to solving a system of linear equations (correct me if there are more): If the system matrix is a full-rank square matrix, you can use Cramer’s Rule; Compute the ...
13
votes
2answers
916 views

Impose the compatibility conditions for mixed finite elements method in Stokes equation

$\newcommand{\v}[1]{\boldsymbol{#1}}$ Suppose we have following Stokes flow model equation: $$ \tag{1} \left\{ \begin{aligned} -\mathrm{div}(\nu \nabla \v{u}) + \nabla p &= \v{f} \\ \mathrm{div} \...
3
votes
1answer
216 views

Using same memory space for global and local Petsc DA Vectors

I have constructed a local and global distributed array in Petsc 3.2 using: DMCreateGlobalVector(da, &v); DMCreateLocalVector(da, &lv); In order to ...
8
votes
1answer
953 views

Fourier transform for Neumann boundary condition

I need to solve system of two coupled partial differential equations numerically. \begin{align} \frac{\partial x_1}{\partial t} &= c_1\nabla ^2 x_1 + f_1(x_1,x_2)\\ \frac{\partial x_2}{\partial ...
10
votes
3answers
332 views

Ways of visualizing event data in search of performance issues

I'm trying to optimize an MPI application with a highly asynchronous communication pattern. Each rank has a list of things to compute, and sends messages as necessary if the inputs or outputs reside ...
7
votes
1answer
495 views

Linearized implicit time stepping

Consider the general FD implicit time stepping scheme $\frac{x_{t+1} - x_t}{\Delta t} = f(x_{t+1})$, where $x$ is the vector variable of interest and $f$ is some function, generally non-linear. ...
7
votes
3answers
1k views

Choosing subset of vectors to approximate a subspace

Suppose I have a high-dimensional vector space $X$, a subspace $V \subset X$, and a collection of $n$ vectors $\{x_i\}_{i=1}^n \subset X$. My question is: How can I choose a small collection $k < ...
3
votes
1answer
48 views

How do I measure the confidence of each new observation according to a decision tree learning model?

I have a decision tree model -- that I've trained with some data. I just got a new data set in and I want to run it through the model. Is there some way I can measure a "confidence interval" for the ...
10
votes
2answers
715 views

Finite difference scheme for “wave equation”, method of characteristics

Consider the following problem $$ W_{uv} = F $$ where the forcing term can depend on $u,v$ (see Edit 1 below for the formulation), and $W$ and its first derivatives. This is a 1+1 dimensional wave ...
4
votes
1answer
1k views

Second order directional derivative in image processing

it is all about valley detection in image processing. I would like to find, for a given pixel, direction for higher second order derivative. I am not quite sure what discrete mask/filter I can use to ...
7
votes
2answers
629 views

transitive floating point comparison with (absolute) tolerance

I want to compare two floating point numbers for equality relative to a known absolute tolerance. However, this is inside an algorithm I wrote quite some time ago, and I believe the logic of that ...
27
votes
5answers
17k views

Permute a matrix in-place in numpy

I want to modify a dense square transition matrix in-place by changing the order of several of its rows and columns, using python's numpy library. Mathematically this corresponds to pre-multiplying ...
5
votes
3answers
10k views

Solving two coupled non-linear second order differential equations numerically

I have encountered the following system of differential equations in lagrangian mechanics. Can you suggest a numerical method, with relevant links and references on how can I solve it, and the ...
12
votes
3answers
306 views

Heuristic check of numerical stability

Assume I have a real valued function $f(x_1,\ldots ,x_N)$ of some variables $x_i$ which I want to evaluate numerically. In general the formula for $f$ can contain products, rationals, trancendental ...
11
votes
4answers
12k views

Fastest PCA algorithm for high-dimensional data

I would like to perform a PCA on a dataset composed of approximately 40 000 samples, each sample displaying about 10 000 features. Using Matlab princomp function consistently takes over half an hour ...
12
votes
1answer
242 views

Algorithms for linear system of ODEs

I wonder: what is the best algorithm to solve \begin{equation} \frac{du}{dt} = Au \end{equation} Where $A$ is a real $n\times n$ matrix. A is not explicitly time-dependent, usually sparse but not ...
11
votes
2answers
2k views

What are the fastest available implementations of BLAS/LAPACK or other linear algebra routines on GPU systems?

nVidia, for example, has CUBLAS, which promises 7-14x speedup. Naively, this is nowhere near the theoretical throughput of any of nVidia's GPU cards. What are the challenges in speeding up linear ...
9
votes
1answer
2k views

Sensitivity of BFGS to initial Hessian approximations

I'm trying to implement the Broyden-Fletcher-Goldfarb-Shanno method to find the minimum of a function. I need two initial guesses $x_{-1}$ & $x_0$ and an initial Hessian Matrix approximation $B_0$...
4
votes
1answer
122 views

Efficient way to find max height repetitive sub-trees in an object tree

I am trying to solve a problem of finding a max repetitive sub-tree in an object tree. By the object tree I mean a tree where each leaf and node has a name. Each leaf has a type and a value of that ...
8
votes
3answers
231 views

How to estimate the impact of small scale on large scale in fluid dynamics?

Assuming that a direct numerical simulation is performed, what is a good method for estimate the impact of small scale on large scale in fluid dynamics ? For example is it pertinent to compare two run ...
8
votes
3answers
3k views

random number generation from cython

I want to make my python program fast by using cython, but my inner loop is still making slow python calls to the random number generator! Several years ago this same issue was raised by someone on ...
4
votes
1answer
3k views

Plotting x,y coordinates and vectors with octave

I have a data set containing the recorded data from a car's motion (latitude,longitude, and heading). I'd like to plot the (lat,lon) points on a 2D plot with a unit vector pointing in the direction ...
10
votes
3answers
3k views

Solution of quartic equation

Is there a open C-implementation for the solution of quartic equations: $$ax⁴+bx³+cx²+dx+e=0$$ I am thinking of an implementation of Ferrari's solution. On Wikipedia I read that the solution is ...

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