# All Questions

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I am reading the following file, that explain the Nelder-Mead optimization Algorithm.(Algorithm Below) Where $B$ is the best point, $G$ second best point, $W$ is the worst point, $R$ reflection point. ...
560 views

### Examples of PDE computations using parallelism in both space and time

In the numerical solution of initial boundary value PDEs, it is very common to employ parallelism in space. It is much less common to employ some form of parallelism in the time discretization, and ...
6k views

### Recommendations for a usable, fast Java matrix library?

This complements an earlier question on usable, fast C++ matrix libraries. I've looked at the Java Matrix Benchmark, and it seems like the performance of java matrix libraries is all over the place. ...
1k views

### Monte Carlo simulation of 3D X-Y model

I need to compute the helicity modulus as a function of temperature for a three-dimensional X-Y model (see N.K. Kultanov, Yu.E. Lozovik, "The critical behavior of the 3D X-Y model and its relation ...
3k views

### How to let OpenFOAM abort a simulation when values exceed a given range?

When the absolute pressure becomes negative or $U$ exceeds the speed of light, things have pretty obviously gone wrong (be that bad boundary conditions, a too coarse mesh, a too large timestep etc.). ...
684 views

### C library - iterative sparse complex linear equation solver?

Where can I find a library to solve a sparse complex matrix equation iteratively in C. So far I've only found libraries for direct solution to complex systems, and libraries for iterative solutions to ...
5k views

### Efficient interpolation method for unstructured grids?

I would like to know a good method for interpolating data between two unstructured grids, where one grid is a coarser version of the other. Efficiency is very important to me since I'm solving a ...
4k views

### How can I approximate an improper integral?

I have a function $f(x,y,z)$ such that $\int_{R^3} f(x,y,z)dV$ is finite, and I want to approximate this integral. I'm familiar with quadrature rules and monte carlo approximations of integrals, ...
88 views

### Produce equation of curve, given some coordinates [duplicate]

Possible Duplicate: Get equation for a curve which intersects x at seemingly randomly distributed points? I tried asking something similar to this before, but I guess I didn't explain very well. ...
1k views

### Libraries for solving Lyapunov's equation

The following matrix equation $$B\Sigma + \Sigma B^T + C = 0$$ in $\Sigma$ $-$ for given $B$ and $C$ matrices $-$ appears in my work as a characterization of a covariance matrix. I have learned that ...
5k views

### Finding which triangles points are in

Suppose I have a 2D mesh consisting of nonoverlapping triangles $\{T_k\}_{k=1}^N$, and a set of points $\{p_i\}_{i=1}^M \subset \cup_{k=1}^N T_K$. What is the best way to determine which triangle each ...
108 views

### Numerically stable real solution(s) to a system of bivariate quadratics

I have a a system of bivariate polynomials as follows: $E(u,v): e_2(u) v^2 + e_1(u) v + e_0(v) = 0 \\ F(u,v): f_2(u) v^2 + f_1(u) v + f_0(v) = 0$ where $e_n(u) = e_{n_2}u^2 + e_{n_1} u + e_{n_0}$ ...
3k views

### What is the most efficient way to diagonalize small matrices?

I have a problem where I need to diagonalize a large number of small Hermitian matrices. Typically the matrices are between 4 and 64 in size (skewed towards the low end) and the number of matrices is ...
618 views

### Finding a permutation that makes a matrix lower triangular

I have a system of linear equations in form of $AX=b$ where $A_{m\times n}$, $X_{n\times 1}$ and $b_{m\times 1}$. Coefficient matrix $A$ is quite sparse. However, using a practical LP solver like ...
1k views

### LP feasibility checking

I have a linear programming problem. I want to know if this LP is feasible. What is the best known algorithm for checking feasibility of an LP or a linear system of equations?
983 views

### Applications of Moore - Penrose generalized inverse of a matrix and associated projection?

I am seeking applications in the industry for the Moore-Penrose generalized inverse $A^\dagger$ of a matrix $A$. The Moore-Penrose Inverse of $A\in \mathbb{C}^{m\times n}$, denoted by $A^\dagger$, ...
2k views

### How to find Lyapunov exponent for coupled system

Answer gives a software for calculating conditional Lyapunov exponent (CLE) for coupled oscillators in chaos synchronization. However, it is hard to follow and there is no graphical output of the ...
204 views

520 views

### Exploring feasible points in a linearly defined space

What is the quickest way to find a point inside a linear feasible space? (Defined by the intersection of several hyperplanes and halfspaces). I want to be able to choose an initial point in the ...
1k views

### Best practice for storing hierarchical simulation data

TL,DR What is the accepted best practice in scientific computing circles for storing large quantities of hierarchically structured data? For example, SQL does not play nicely with large sparse ...
236 views

### CFD for high-detailed turbulence and non-linear waves

What are typical (or promising) techniques and methods in CFD to achieve high-detailed turbulence and non-linear waves interaction? And with "active" geometry (when bodies interacts with fluid in both ...
1k views

### What are the strategies for local Adaptive Mesh Refinement (local AMR) on unstructured meshes?

I am interested in local AMR on unstructured meshes. Currently, I'm working with the OpenFOAM library - it supports completely unstructured local AMR: cell refinement criteria determine a list of ...
1k views

### Approximate spectrum of a large matrix

I want to compute the spectrum (all the eigenvalues) of a large sparse matrix (hundreds of thousands of rows). This is hard. I am willing to settle for an approximation. Are there approximation ...
2k views

### eigenvalues (and determinant) of a hadamard product of matrices

I need to compute the determinant of a matrix that is calculated as $B \circ A$, with $B$ and $A$ being square matrices and $\circ$ representing their Hadamard product. One way of doing this is ...
1k views

### SVD for finding the largest eigenvalue of a 50x50 matrix — am I wasting significant amounts of time?

I've got a program that computes the largest eigenvalue of many real symmetric 50x50 matrices by performing singular-value decompositions on all of them. The SVD is a bottleneck in the program. Are ...
1k views

### f2py: error f90 not supported by GnuFCompiler needed for source_file.f90

I'm trying to install a Python package that relies on extensions built from Fortran 90 using f2py, but I get the following error: ...
311 views

### Computing Permanents of $64 \times 64$ Matrices

I need to compute the Matrix Permanents of several $64 \times 64$, zero-one matrices. I have tried using the built in functions in both Sage and Maple, but both programs return out of memory errors. I ...
594 views

### What algorithm for solving a set of stiff ODEs would be easiest to port to high precision floating point arithmetic?

I want to solve a relatively small system of stiff ODEs (< 10 first-order equations) using high precision floating point arithmetic (using MPFR or alike). What would be the easiest algorithm to ...
3k views

### Drawbacks of Newton-Raphson approximation with approximate numerical derivative

Suppose I have some function $f$ and I want to find $x$ such that $f(x)\approx 0$. I might use the Newton-Raphson method. But this requires that I know the derivative function $f'(x)$. An analytic ...
277 views

### efficiently solving a low rank linear parametric systems?

I have a large number of systems of the form: $Ax=b_i$ To solve for a large numbers of such $b_i\;1\leq i \leq k$ but where $A$ is fixed (A is a rank $p$ general --i.e. non sparse, non PSD-- ...
216 views

### Different kinds of Integral Equation Methods

I am relatively new to integral equations for solving time-harmonic EM scattering problems. I have read a decent number of papers on the subject, and it seems that for formulations that can support 3D ...
386 views

### Get equation for a curve which intersects x at seemingly randomly distributed points?

Is there any type of function that when graphed would show a curve which intersects the x axis multiple times, with each point being an arbitrary distance from the last? I mean, not like a trig ...
9k views

### Interpolate 2D data

I generated a cartesian grid in Python using NumPy's linspace and meshgrid, and I obtained some data over this 2D grid from an ...
8k views

### Is there an in practice limit on the number of constraints on a linear programming problem?

I am new to linear programming and have formulated a linear program (LP) with order of $10^{13}$ variables and $10^{13}$ constraints, although the constraint matrix is extremely sparse. I wanted to ...
1k views

### How to numerically calculate residues?

I need to calculate the following integral: $${1\over 2\pi i} \int_C f(E) \, d E$$ $$f(E) = {\rm Tr}\,\left(({\bf h} + E)\,{\bf G}(E) \right)$$ Where $\bf h$ is a matrix (one particle kinetic and ...
807 views

### How to handle large numbers of output data sets from a simulation/sensitivity analysis?

Somewhat related, but I think the question is distinct enough to justify a separate question. As a bit of background, I come from a observational/statistical Epidemiology background, working with ...
891 views

### How do I make sure that the results of my simulations and the results in my paper are always in sync?

In one of my papers, I list some numerical results in addition to some figures. What I'd like to do is make sure that the numerical results in my paper always agree with the code. Right now, I just ...
4k views

### Specifying boundary conditions for imported mesh in OpenFOAM

I have a mesh produced from scanning a real 3D object (I don't have a geometry). What is the most convenient way to specify inlets, outlets, etc. for CFD in OpenFOAM? The mesh consists of thousands of ...
3k views

### How do I know if my code is being vectorized by the compiler?

As exemplified by Jed Brown's answer to Costs of lookups versus calculations, using vectorized vs non-vectorized floating point operations results in much faster code. Many modern compilers claim ...
823 views

I'm having some troubles implementing a collocation method to solve a stochastic partial differential equation of the form: $\nabla (a(x,w)\nabla u(x,w))=f(x,w)$ in $D$, $u=g$ in $\partial D$ where $... 1answer 77 views ### Computing a sequence of row interchanges that realizes a given permutation matrix? This question is aimed at cleaning up an implementation detail of an in-house sparse direct solver. It uses METIS to reorder$A$into$PAP^{T}$for reduced fill-in. Inside the$Lx=b$and$L^{T}x=b$... 2answers 8k views ### Null-space of a rectangular dense matrix Given a dense matrix $$A \in R^{m \times n}, m >> n; max(m) \approx 100000$$ what is the best way to find its null-space basis within some tolerance$\epsilon$? Based on that basis can I then ... 1answer 292 views ### Should I include integral constraints in a integer linear program with a totally unimodular constaint matrix? I have formulated an integer linear program (ILP). The constraint matrix for the ILP is totally unimodular. Should I solve it as an LP without the integral constraints, or should I keep the integral ... 2answers 924 views ### How to detect key turning points on a driven road? I am looking for a description of algorithm which allows me to detect key turning points on the road amongs a set of all given points. I've ilustrated my problem on the below image: Green spots: ... 1answer 256 views ### Defining electric current source excitations for surface integral equation formulations In a finite difference (FD) based electromagnetic formulation based on a Yee cell grid, one can define electric current source excitations ($J$) on the$E$field grid points. At a distance, the fields ... 2answers 178 views ### Predict runtimes for dense linear algebra I would like to predict runtimes for dense linear algebra operations on a specific architecture using a specific library. I would like to learn a model that approximates the function$F_{op} \;::\; $... 1answer 607 views ### Quality open source AMR libraries [duplicate] Possible Duplicate: Is there a general-purpose library for structured grid adaptive mesh refinement? I'm looking for a quality, open source, maintained, scalable automated mesh refinement library ... 4answers 2k views ### What tools or approaches are available to speed up code written in Python? Background: I think I might want to port some code that calculates matrix exponential-vector products using a Krylov subspace method from MATLAB to Python. (Specifically, Jitse Niesen's expmvp ... 2answers 1k views ### Line search for Newton method If we want to solve nonlinear minimization problem $$\min_{x} f(x),$$ making least-squares assumption and using Gauss-Newton method so that at k$th$iteration we have:$\$J_k^T J_k p_k = - J_k^T ...

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