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3
votes
1answer
150 views

What is a good introduction to mixed quantum-classical modelling

Currently, I have some experience with classical molecular dynamics simulations, and I've had undergraduate course in quantum mechanics (the course was "analytical" one, no approaches to computer ...
15
votes
4answers
1k views

Testing numerical optimization methods: Rosenbrock vs. real test functions

There seem to be two main kinds of test function for no-derivative optimizers: one-liners like the Rosenbrock function ff., with start points sets of real data points, with an interpolator Is it ...
4
votes
0answers
105 views

Existing software/scripts for spiral graphs?

I am looking for existing software or scripts to generate spiral graphs from cyclical (time) data, as presented by Webber and Muller. The graphs shown in the paper look like a great means of ...
2
votes
1answer
132 views

Factor a non-symmetric matrix into the product of a sparse symmetric matrix and a diagonal matrix plus a low rank correction

I have a non-symmetric matrix, where the non-symmetry only appears at a subset of points. This arises due to the particular manner on which boundary conditions are applied in a Cartesian grid method. ...
2
votes
1answer
138 views

Numerically designing a periodic 1D curve that maximizes an integral area objective and satisfies value, derivative, and frequency constraints

I need to write MATLAB program (or use an existing one) to obtain Fourier series coefficients. Let's say the series is going to approximate a 1D curve. The boundary conditions are: value of the ...
12
votes
1answer
738 views

Numerical Methods for the Schrodinger Equation

We are comparing the performance of various numerical methods that can be used to solve the Schrodinger's Equation for the Hydrogen Atom interacting with a strong laser pulse (too strong to use ...
16
votes
2answers
1k views

Boost::mpi or C MPI for high performance scientific applications?

The thing I dislike most about MPI is dealing with datatypes (i.e. data maps/masks) because they don't fit that nicely with object oriented C++. boost::mpi only ...
3
votes
2answers
218 views

How to efficiently compute the total least squares with an inequality constraint

I am looking for an efficient method to compute $$\sum_{i=1}^\left|B\right|\left|Ax_i-b_i\right|^2\rightarrow min$$ under the condition $$\forall i, x_i\ge 0,$$ where $A$ is an n-by-m matrix and $B$ ...
3
votes
2answers
246 views

Positive semi-definiteness of a (symmetric) matrix

Suppose a matrix $A\in\mathbb{R}^{n\times n}$ is given. Faced with a proof for $$x^TAx>0,$$ for a non-zero vector $x\in\mathbb{R}^{n}$, I was thinking to use the information of the spectrum of $A$ (...
7
votes
1answer
1k views

Termination Criterion of Golden Section Search

Reading an implementation of the golden section search, I came across the following termination test: $$| a - d | < \varepsilon ( |b| + |c| )$$ where $a < b < c < d$ are four points at ...
5
votes
1answer
911 views

Is the heat equation with Neumann boundary conditions well-posed?

For example I consider a heat equation that I want to solve numerically : $$u_t=u_{xx},$$ In order to have a uniqueness on a computational bounded domain I have to have boundary condition specified ...
5
votes
1answer
116 views

How to assure that a number only contains a certain range of digits?

Say I would like to generate a pseudo-random number, which only contains the digits 1, 4, 7 (this is arbitrary). My first guess would be to create and array "147" and create random numbers in the ...
10
votes
3answers
472 views

Priorities for learning computational methods, when should I write my own code vs. using libraries as a beginning graduate student?

I am beginning my graduate studies in engineering and will be working on computational science projects. I noticed that there has been some discussion about the advantages and disadvantages of ...
34
votes
3answers
112k views

What is the simplest way to do a user-local install of a python package?

I don't want to deal with virtualenv for a local Python installation, I just want to install a few packages locally without dealing with the PYTHONPATH environment ...
1
vote
1answer
4k views

Is it possible to access a GPU remotely (i.e., from another machine)? [closed]

I want to access a GPU on a computer remotely, and share this GPU with different desktops. I envision this sort of access as being similar to using a VNC. Is it possible to do something like what I've ...
3
votes
1answer
611 views

parametric linear programming

I have a linear programming problem min $c^T x$ $Ax\leq b$ However, in my problem, $A$ contains also some variables $y$, e.g. $$A = \begin{pmatrix} y_1 & 4 \\ 3 & y_2 \end{pmatrix}$$ I ...
2
votes
2answers
128 views

Handling inconsistent solutions obtained by PCA

In order to achieve a 2D representation $X\in\mathbb{R}^{n\times 2}$ of some high-dimensional data residing in $Y\in\mathbb{R}^{n\times k}$, I use PCA:$$X=Y\cdot U,$$where $U\in\mathbb{R}^{k\times 2}$ ...
3
votes
0answers
459 views

How do I configure PETSc to run long double precision or some other precision that is greater than default? [closed]

I'm installing PETSc for complex numbers with the C99 standard. I'd like to have it installed using a higher precision than the default (double, I presume) since that will most likely make the LU ...
7
votes
2answers
863 views

Can all eigenvalues of a Hermitian Toeplitz matrix be computed in $\tilde{O}(n)$ time?

I know there are "superfast" $O(n \log^p n)$ algorithms for solving Toeplitz linear systems. Is it possible to compute all eigenvalues of such a matrix with the same complexity?
0
votes
1answer
214 views

Drawing 3d projection of complex surface

I have a complex surface (real dimension 2) in $\mathbb{C}^2$ with coordinates $(z,w)$ given explicitely: for any $\xi \in \mathbb{C}$ I know points $w(\xi)$ of intersection of surface with complex ...
2
votes
2answers
551 views

Binary Integer Programming Problem Subject to a Set of First-Order DEs

Recently, I came across an optimization problem with binary decision variables which was constrained with a set of first-order differential equations (resulting from a continuous-time Markov chain ...
6
votes
2answers
522 views

Recommendations for a usable, fast GPL-compatible derivative-free numerical optimization library that can be interfaced to C++

I am dealing with optimization of functions for which I do not have derivatives available, and the optimization is not constrained. I am searching for a high quality GNU Public License-compatible ...
3
votes
2answers
948 views

How to compute the optimal ridge regression model

I found R function ridge.cv very useful. I would like to implement the equivalent function in MATLAB. As a starting point, I used MATLAB function ...
8
votes
1answer
2k views

PDE discretization with the method of rothe and the method of lines (Modular implementation)

The Heat equation is discretized in space with FV (or FEM), and a semi-discrete equation is obtained (system of ODEs). This approach, known as the method of lines, allows to easily switch from one ...
1
vote
1answer
83 views

Normalizing axes prior to PCA

For a given centered configuration of points $X\in\mathbb{R}^{n\times 3}$, the covariance matrix is denoted by $S=\frac{1}{n}X^TX$. Recall that the 2D PCA solution is obtained by $Y=X\cdot U$, where $...
1
vote
1answer
387 views

How to find the number of principal components that lead to the smallest generalization error?

I am working on a paper part of which is the application of validation rules to find how many principal components give us the least generalization error. The concept goes more or less like this: "...
3
votes
2answers
1k views

Evaluation of multivariate polynomials

I am seeking for an efficient algorithm to compute a multivariate polynomial of a fixed structure, but different coefficients and evaluation points. The question is the same as this one, which ...
5
votes
3answers
586 views

Manipulating Matrices in Matlab

Suppose I have a matrix $A$ of size $n_1 \times n_2 \times n_3$ Now, I have another matrix $B$ of size $n_1 \times n_2 \times n_3 \times N$ where $N<n_3$ I'd like to create the following matrix ...
0
votes
1answer
71 views

Relation to all-pairs Euclidean distances

Given $d$-dimensional coordinates residing in a matrix $X\in\mathbb{R}^{n\times d}$, the Euclidean distance between items $i$ and $j$ is denoted as $g_{ij}$. Let $c\in\mathbb{R}^d$ denote the centroid ...
5
votes
2answers
558 views

Interpolation schemes to move data between cells and nodes

I work on non-graded quadtree grids where the entire grid is a hierarchy of cells specified using a quadtree data structure, where, in general, there is no constraint regarding the relative size of ...
4
votes
2answers
980 views

Algorithmically selecting colors that will contrast with their background

I am trying to write an implementation of a color quantization algorithm in order to find an image's dominant colors (say 5) and then find contrasting colors based on the colors found in the image. I'...
3
votes
4answers
10k views

Estimating the Courant number for the Navier-Stokes Equations under differing Reynolds number regimes

I am familiar with the Courant-Friedrich-Lewy Condition in as far as it applies to the stability of explicit finite difference schemes for standard parabolic and hyperbolic PDEs. However, when ...
1
vote
1answer
281 views

Fast Algorithms for solving sparse LP problems

For solving a very sparse LP: {min $cx$: s.t.: $A_{m \times n}x=b$ , $x\geq 0$}, which one of the following algorithms is faster? Logarithmic barrier method Other variants of the interior point ...
2
votes
1answer
81 views

Rational LP to integer LP

In the worst case complexity analysis of all the polynomial algorithms in linear programming such as ellipsoid method and interior point method, there is an assumption that the input data must be ...
11
votes
2answers
3k views

Eigenvalue decomposition of the sum: A (symmetric) + D (diagonal)

Suppose $A$ is a real symmetric matrix and its eigenvalue decomposition $V \Lambda V^T$ is given. It is easy to see what happens with the eigenvalues of the sum $A + cI$ where $c$ is a scalar constant ...
6
votes
2answers
4k views

When to stop Gauss-Seidel-iterations?

I want to have an estimation, that my solution has an error, let's say less than 1e-8. Usually, I stop the Gauss-Seidel algorithm, when the residual is "small enough" and this is already the problem. ...
9
votes
2answers
1k views

Is there an algorithm to find an almost-convex hull given a tolerance angle?

I'd like to know if there is an algorithm that given a set o points and an angle computes the convex-hull if the angle is $\alpha = 0$ and given an $\alpha > 0$ computes an envelope that follows ...
6
votes
1answer
234 views

How far is a non-symmetric discretization of an elliptic operator from the continuous operator itself?

I am investigating the accuracy and stability properties of a non-symmetric discretization of a Poisson problem. The problem originates from a ghost fluid discretization of the projection step of a ...
2
votes
0answers
1k views

Can post-processing use topoSet and createPatch without screwing up the results?

I would like to use patchAverage to obtain the average pressure on an object that consists of multiple patches (due to different boundary conditions), however ...
10
votes
3answers
1k views

Basin of attraction for Newton's method

Newton's method for solving nonlinear equations is known to converge quadratically when the starting guess is "sufficiently close" to the solution. What is "sufficiently close"? Is there literature ...
3
votes
3answers
924 views

Is busy waiting on both MPI_Iprobe and MPI_Testsome efficient?

I have an MPI application that needs to asynchronously respond to both incoming messages and request completions inside a dedicated communication thread. The obvious way to do this is a busy wait ...
10
votes
3answers
998 views

Explicit Euler method too slow for reaction-diffusion problem

I am solving Turing's reaction-diffusion system with following C++ code. It is too slow: for 128x128 pixel texture, acceptable number of iterations is 200 – which results in 2.5 seconds of delay. I ...
11
votes
1answer
655 views

Solving huge dense linear system?

Is there any hope in solving the following linear system efficiently with an iterative method? $A \in \mathbb{R}^{n \times n}, x \in \mathbb{R}^n, b \in \mathbb{R}^n \text{, with } n > 10^6$ $Ax=...
5
votes
1answer
842 views

Convex polytope volume and centroid calculation

I have troubles imagining how to compute a volume and centroid of an n-dimesional convex polytope. For a polygon (especially for convex polygon) the area and centroid are described in (wiki) by $$ A=...
8
votes
2answers
2k views

Nonblocking version of MPI_Barrier in MPI 2

I have a bunch of MPI processes exchanging request messages back and forth. Processes do not know which other processes will send them messages, or how many. Given this situation, I want an ...
8
votes
2answers
208 views

How should I report profiling/timing information about my code?

I've seen a lot of publications in Computational Physics journals use different metrics for the performance of their code. Especially for GPGPU code, there seems to be a great variety of timing ...
29
votes
7answers
7k views

Alternatives to Journal of Computational Physics

The Journal of Computational Physics has been an important outlet for computational science in the past, and I have published there before. For the benefit of those (like me) who have signed the ...
8
votes
1answer
2k views

Finite difference coordinate transformation for spherical polar coordinates

I have part of a problem that is described by the momentum conservation equation: $\frac{\partial \rho}{\partial t} + \frac{1}{\sin\theta} \frac{\partial}{\partial \theta}(\rho u \sin \theta) =0$ ...
6
votes
3answers
138 views

How can I detect which among N bodies with different velocities will collide?

Suppose I have N different airplanes traveling on a two dimensional rectangular plane of size 400km x 400km (i.e. it is as if all planes travel at the same altitude). Assume each airplane has a ...
17
votes
5answers
6k views

What is the best way to determine the number of non zeros in sparse matrix multiplication?

I was wondering whether there is a fast and efficient method to find the number of non zeros in advance for sparse matrix multiplication operation assuming both matrices are in CSC or CSR format. I ...

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