# All Questions

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### 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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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)?
278 views

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\... 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 ... 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, ... 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 &... 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 ... 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 (... 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-... 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 ... 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 ... 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 ... 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 \... 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 ... 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: ... 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 ... 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... 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 ... 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 ... 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 ... 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 ... 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? 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 ... 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 (... 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}}.$$I know that running the parallel code on one ... 1answer 310 views ### Working with multi-dimensional functions How would you represent functions of type [-1, 1]^n \to \mathbb R \; for moderate n? How would you integrate them? For small n (1-2) such functions can be represented as histograms, vectors in ... 3answers 911 views ### Which linear algebra texts should I read before learning numerical linear algebra? Assuming one wishes to study numerical linear algebra in depth (and follow journals on numerical linear algebra and matrix theory), which would be a better course/better book to take up at first: ... 2answers 2k views ### What's the most efficient way to compute the eigenvector of a dense matrix corresponding to the eigenvalue of largest magnitude? I have a dense real symmetric square matrix. The dimension is about 1000x1000. I need to compute the first principal component and wonder what the best algorithm to do this might be. It seems that ... 3answers 1k views ### Drawing samples from a finite mixture of normal distributions? After some Bayesian update steps, I am left with a posterior distribution of the form of a mixture of normal distributions,$$\Pr(\theta| \text{data} ) = \sum_{i=1}^k w_i N(\mu_i, \sigma^2).$$That is, ... 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 ... 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 ... 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 ... 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: ... 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 ... 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 ... 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 ... 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) ...