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13
votes
5answers
955 views

On Finding Open Source Projects To Contribute To

This question has been asked a billion times on Stackoverflow however, the focus has always been on Non-Numerical Coding. I am looking for a project to contribute to within the confines of Numerical ...
4
votes
2answers
172 views

What mapping strategy should I use when solving many large linear systems of equations?

I am working on a problem that involves solving many (thousands) of distinct linear systems of equations, each with thousands of variables. Let's assume that the size of each matrix is exactly the ...
15
votes
1answer
691 views

Are there any open source inverse-based multilevel ILU implementations?

I am very impressed with the serial performance of multilevel inverse-based ILU preconditioners, particularly for heterogeneous Helmholtz, but I am surprised to not be able to find any open source ...
74
votes
6answers
17k views

How much better are Fortran compilers really?

This question is an extension of two discussions that came up recently in the replies to "C++ vs Fortran for HPC". And it is a bit more of a challenge than a question... One of the most often-heard ...
7
votes
1answer
174 views

Conjugate Gradient with Hierarchical Basis Functions: How can the hierarchical base be decomposed?

I'm trying to implement a Conjugate Gradient solver using Hierarchical Basis Functions, following this paper. In section 3 the paper says that the hierarchical basis matrix $S$ can be decomposed into ...
2
votes
1answer
197 views

Power series approximation for any function such as $-e^{x^{2}}$ in some easily-accessed open-source software?

My comrades repeatedly encourages monotonous problems where the issue is the same: chain-rule and some basic arithmetic. Is there some computational way to derive power series approximations? Suppose ...
8
votes
4answers
2k views

Are open-source codes available to study protein folding?

I would like to test the influence of solvation parameters in implicit solvation models and wonder which codes are freely available as standalone programs for protein folding of small proteins, and ...
7
votes
2answers
144 views

Can quantum methods be applied to the protein-ligand docking problem?

In the problem of protein-ligand docking, most of the time people are happy if they can just predict the final conformation the ligand adopts into the protein's binding pocket. Most of the time one ...
8
votes
1answer
252 views

Adaptive mesh refinement with perfectly matched layers?

We have an adaptive mesh refinement (AMR) code for solving the elastic wave equation with frictional fault interfaces (based on Chombo for those that are interested). One of the things that we have ...
14
votes
2answers
2k views

How useful is PETSc for Dense Matrices?

Wherever I have seen, PETSc tutorial/documents etc. say that it is useful for linear algebra and usually specifies that sparse systems will benefit. What about dense matrices? I am concerned about ...
5
votes
2answers
484 views

Implementing a fair scheduling policy on Maui/Torque

We have Maui and Torque on our lab's UNIX cluster. Right now, all jobs are served by FIFO. We'd like to implement a more fair policy, but I have not successfully implemented it. The online ...
4
votes
1answer
658 views

Diffusion kernel “guide”

Diffusion kernels are kernels which "project" information about graphs into $R^n$ so that certain machine learning techniques can be performed. I have read through this paper and feel fairly ...
6
votes
3answers
228 views

Is it possible to use BLAS if I have a function rather than a matrix?

My matrix sizes have grown beyond what can fit on the RAM but I have a function which defines each element cheaply. Is it possible use BLAS (in Fortran or even in MATLAB) in such cases? If I had a ...
4
votes
1answer
232 views

What is the difference between ECPs and ADF frozen cores?

As the title suggests, what are the differences between the frozen core approximation as implemented by Amsterdam Density Functional and effective core potentials (ECPs)?
8
votes
2answers
278 views

One-sided non-linear least squares with linear constraints

I am trying to solve a one-sided non-linear least-squares problem with linear constraints, i.e the problem: $\min_{\mathbf{x}} \quad \sum^m_{i=1} \mathbf{r}_i(\mathbf{x}) \qquad \text{ s.t } \quad A\...
8
votes
1answer
359 views

Red(-Green)-Refinement vs. Newest-Vertex-Bisection

What are the "Pros and Cons" for these two methods of mesh-refinement? Both seem to be the prevalent methods. I can naturally imagine that global red refinement is comparatively easy to implement and ...
52
votes
7answers
6k views

What core skills should every computational scientist have? [closed]

Every scientist needs to know a bit about statistics: what correlation means, what a confidence interval is, and so on. Similarly, every scientist ought to know a bit about computing: the question is, ...
5
votes
5answers
12k views

How can I plot piece-wise defined function in some easily-accessed open-source tool?

I want to plot $$f_{n}(x) = \begin{cases} x-n & \text{for } n \leq x \leq n+1 \\ 2-x+n & \text{for } n+1\leq x \leq n+2 \\ 0 &...
3
votes
2answers
2k views

How does Gaussian 09 handle 'Frozen Core Approximations' and how does it compare to CFour handling?

Background I'm currently working with two quantum software packages: Gaussian 09 and CFour. CFour does a very good job giving explicit control over how you want to invoke frozen core approximations ...
10
votes
3answers
837 views

Can I use an explicit time stepping scheme to determine numerically whether an ODE is stiff?

I have an ODE: $u'=-1000u+sin(t)$ $u(0)=-\frac{1}{1000001}$ I know that this particular ODE is stiff, analytically. I also know that if we use an explicit (forward) time stepping method (...
18
votes
3answers
2k views

What guidelines should I use when searching for good preconditioning methods for a specific problem?

For the solution of large linear systems $Ax=b$ using iterative methods, it is often of interest to introduce preconditioning, e.g. solve instead $M^{-1}(Ax=b)$, where $M$ is here used for left-...
24
votes
4answers
7k views

How to add large exponential terms reliably without overflow errors?

A very common problem in Markov Chain Monte Carlo involves computing probabilities that are sum of large exponential terms, $ e^{a_1} + e^{a_2} + ... $ where the components of $a$ can range from ...
10
votes
2answers
799 views

Which journals should I read to keep up on advances in solving PDEs numerically?

I solve a lot of PDEs numerically, but applied math isn't my field. I haven't picked up on which applied math journals I should read to keep up with recent developments in the field. What are good ...
3
votes
1answer
849 views

Is a checkerboard block decomposition of a matrix useful when solving a linear system with a parallel conjugate gradient method?

According to these lecture notes, a checkerboard block decomposition should exhibit better scalability when applied to parallel matrix-vector multiplication (presumably because of greater cache hit ...
11
votes
1answer
1k views

How can I compute a basis for a matrix Lie algebra given a finite set of generators?

Given an arbitrary set of (numerical) square complex matrices $\mathcal{A}=\{A_1,A_2,\cdots,A_m\}$, I am interested in computing the real matrix Lie algebra generated by $\mathcal{A}$, call it $\...
8
votes
1answer
505 views

What's the right way to compare vectors in floating-point?

I know that I should use a tolerance for comparing floating point numbers. But for comparing vectors, I can think of 3 possible solutions corresponding to different distance metrics: Compare the ...
6
votes
5answers
426 views

Where do dense matrices occur?

I have primarily dealt with Dense Matrices arising from Electrodynamics. However, I am interested in knowing where else Dense Matrices occur. I am especially interested in knowing where they occur in: ...
6
votes
2answers
2k views

How can I generate half-normal variates in MATLAB?

I can find the random('normal', 0, 1, 10000,1) command in MATLAB but it generates half-normal variates. I would like to generate random half-normal variates. The ...
5
votes
3answers
745 views

Seemingly non-unique Cholesky factor via QR rectangularisation

I am trying to implement an algorithm from a paper which makes use a QR factorization of a real matrix $A$ as a means of one of forming the Cholesky factor of $A^T A$ without explicitly forming $A^T A$...
4
votes
2answers
747 views

Outputting a distributed vector in PETSc

I'm working with someone else's code that uses PETSc 3.0.0-p9. They have a vector at the end of the computation that is distributed among a number of different processors, and I want to output that ...
17
votes
8answers
1k views

Is there any open-source or easy-to-access software that can simplify algebraic expressions like $x^{2}+2x+3, x=\sqrt{2}t-1$?

I always calculate things by hand, but now my comrades are getting nasty and making a lot of repetitive exercises involving just plugging things in like the expression above. I am particularly ...
6
votes
2answers
1k views

Starting multiple processes from a single PBS job and distributing them on the free cluster nodes

I'm not very familiar with PBS (we have torque installed here), and I have only used it to run one process per job so far, so bear with me. The actual problem I am trying to use Mathematica on a ...
5
votes
0answers
2k views

Two-chordless cycle extraction from a failed comparability graph recognition

I have implemented a comparability graph recognition algorithm from M.C. Golumbic's "Algorithmic graph theory and perfect graphs" book. It is hinted in Fekete, Schepers, and van der Veen's "Exact ...
2
votes
1answer
172 views

How can I set different axes for different plots in gnuplot?

I want to plot a few sets of data points on the same x-axis that have different units. How can I set different axes for each incompatible quantity?
5
votes
2answers
1k views

Sufficient conditions to ensure convergence of the conjugate gradient method

I know that a conjugate gradient method is guaranteed to converge to the solution of a linear system if the matrix is positive definite. I'm working with a family of matrices that have the following ...
23
votes
3answers
3k views

What is the principle behind the convergence of Krylov subspace methods for solving linear systems of equations?

As I understand it, there are two major categories of iterative methods for solving linear systems of equations: Stationary Methods (Jacobi, Gauss-Seidel, SOR, Multigrid) Krylov Subspace methods (...
8
votes
2answers
1k views

How do I compute the parallel overhead of a parallel code run on a single processor when no sequential code is available?

I'm profiling the performance of PETSc's linear solvers. As I understand it, $$\text{speedup}=\frac{\text{Sequential Time}}{\text{Parallel Time}}.$$ I know that running the parallel code on one ...
5
votes
1answer
310 views

Working with multi-dimensional functions

How would you represent functions of type $[-1, 1]^n \to \mathbb R \;$ for moderate $n$? How would you integrate them? For small $n$ (1-2) such functions can be represented as histograms, vectors in ...
11
votes
3answers
911 views

Which linear algebra texts should I read before learning numerical linear algebra?

Assuming one wishes to study numerical linear algebra in depth (and follow journals on numerical linear algebra and matrix theory), which would be a better course/better book to take up at first: ...
10
votes
2answers
2k views

What's the most efficient way to compute the eigenvector of a dense matrix corresponding to the eigenvalue of largest magnitude?

I have a dense real symmetric square matrix. The dimension is about 1000x1000. I need to compute the first principal component and wonder what the best algorithm to do this might be. It seems that ...
10
votes
3answers
1k views

Drawing samples from a finite mixture of normal distributions?

After some Bayesian update steps, I am left with a posterior distribution of the form of a mixture of normal distributions,$$\Pr(\theta| \text{data} ) = \sum_{i=1}^k w_i N(\mu_i, \sigma^2).$$ That is, ...
3
votes
1answer
197 views

Can BFGS be used to minimise several functions at once?

I have multiple objective functions which are related to several parameters. I want to minimise more than one objective functions using several parameters. Is it even possible using BFGS? When I used ...
22
votes
4answers
3k views

When do orthogonal transformations outperform Gaussian elimination?

As we know, orthogonal transformations methods (Givens rotations and Housholder reflections) for systems of linear equations are more expensive than Gaussian elimination, but theoretically have nicer ...
18
votes
1answer
2k views

How can wavelets be applied to PDE?

I would like to learn how wavelet methods can be applied to PDE, but unfortunately I do not know a good resource to learn about this topic. It seems that many introductions to wavelets focus on ...
2
votes
1answer
1k views

How to measure the overall performance of a PETSc program using the -log_summary flag?

When I run a PETSc example in parallel with the flag "-log_summary", the first two tables of information look something like this: ...
15
votes
1answer
434 views

How effective is the 'tendrils of knowledge' approach to Comp. Sci?

I was reading this on Math SE. The basic question is : Assume that someone wishes to study something advanced; one way to do this would be to start off from basics and build up. But the "bigger ...
15
votes
4answers
590 views

What are some applications which require interval arithmetic?

I have a very basic notion about interval arithmetic (IA), but it seems to be a very interesting branch of computational science both theoretically and practically. It is clear that the obvious ...
20
votes
6answers
3k views

Analyzing Numerical Error in C++ Function

Suppose that I have a function that takes as input several floating-point values (single or double), does some computation, and produces output floating-point values (also single or double). I am ...
36
votes
4answers
29k views

How does the MATLAB backslash operator solve $Ax=b$ for square matrices?

I was comparing a few of my codes to "stock" MATLAB codes. I am surprised at the results. I ran a sample code (Sparse Matrix) ...
3
votes
1answer
1k views

Problems running a PETSc example in parallel

After configuring and building PETSc, I have successfully been able to run several examples. In particular, I am working with this example. I have been able to run the program using the following ...

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