# Computational Science Stack Exchange Community Digest

## Top new questions this week:

### why is A*v+B*v faster than (A+B)*v?

$A$ and $B$ are $n \times n$ matrices and $v$ is a vector with $n$ elements. $Av$ has $\approx 2n^2$ flops and $A+B$ has $n^2$ flops. Following this logic, $(A+B)v$ should be faster than $Av+Bv$. ...

linear-algebra matlab matrix asked by Sam C. 30 votes answered by Brian Borchers 57 votes

### Example where autodiff works but symbolic differentiation will not?

According to the survey paper on autodiff (linked) Autodiff works on inputs that cannot be specified in closed form but can be described by a sequence of code, each component of which is ...

symbolic-computation automatic-differentiation differentiation asked by Lucas Roberts 12 votes answered by Chris Rackauckas 8 votes

I'm trying to compute efficiently the following \begin{equation} A_j = \sum_{l'=1}^{\infty}\sum_{k= 0}^{K-1} L_{l'}T_ke^{2\pi i \frac{k}{K}j}\epsilon_{l',k} \end{equation} for $j = 0,1, \ldots, ... fourier-transform fftw convolution asked by HansimGlück 4 votes answered by Ian Bush 2 votes ### Why the two Gram-Schmidt algorithms produce different results for qr factorization? For the qr factorization using classic Gram-Schmidt algorithm, I found the 2 different implementations below. The first one uses the for loop to compute the upper triangular matrix R, but the second ... matlab matrix-factorization qr-factorization gram-schmidt asked by sunshine 4 votes ### Why the solid FEM problem can not be solved after constraining 3 degrees of freedom? I write a simple MATLAB code for solving solid FEM problem. The problem looks like that (1) (2) x-------x | / | | / | | / | x-------x (3) (4) Each node has two degrees of ... finite-element matlab solid-mechanics asked by Xu Hui 4 votes answered by Bill Greene 5 votes ### Memory Management - Why certain initializations order are faster? #include <stdio.h> #include <stdlib.h> #include <sys/time.h> float timedifference_msec(struct timeval t0, struct timeval t1) { return (t1.tv_sec - t0.tv_sec) * 1000.0f + ... c memory-management asked by TVSuchty 3 votes answered by Anton Menshov 8 votes ### Solving saddle point problem having non-invertible top-left block with a PETSc nested matrix My system is a symmetric FE problem with lagrange multipliers:$Z=\begin{pmatrix}A & C^T \\ C & 0\end{pmatrix}$The matrix$A$is positive semi-definite, non-invertible. The whole matrix is ... finite-element petsc preconditioning krylov-method saddlepoint asked by janou195 3 votes ## Greatest hits from previous weeks: ### How to code in Matlab: If an argument is empty, then default to "x" value? I have a function with a number of arguments, but some of them are optional. 1.) If when the function is called, some are left empty, how do I code it so that it defaults to a specific value? 2.) ... matlab asked by AlanH 7 votes answered by Nat Wilson 7 votes ### Visualising Maxwell's equations using MATLAB I asked this question to help me understand what is going on in one of Maxwell's equations. I am happy with following through the maths on paper now, but would like to use MATLAB to take it one step ... matlab pde visualization plotting electromagnetism asked by Steve Hatcher 4 votes answered by nicoguaro 10 votes ### What kinds of problems lend themselves well to GPU computing? So I've got a decent head for what problems I work with are best one in serial, and which can be managed in parallel. But right now, I don't have much of an idea of what's best handled by CPU-based ... gpu asked by Fomite 86 votes answered by Max Hutchinson 64 votes ### What is the purpose of the test function in Finite Element Analysis? In the wave equation: $$c^2 \nabla \cdot \nabla u(x,t) - \frac{\partial^2 u(x,t)}{\partial t^2} = f(x,t)$$ Why do we first multiply by a test function$v(x,t)$before integrating? finite-element asked by Andy 13 votes ### Limitations of Density Functional Theory as a computational method? This question arises from the need I have to prepare a lesson on the limitations of Density Functional Theory as a computational approach. I would like to know not only the limitations, but also ... density-functional-theory asked by Stefano Borini 8 votes answered by Dan 10 votes ### 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 ... fluid-dynamics stability asked by Paul 3 votes answered by David Ketcheson 5 votes ### Is there a high quality nonlinear programming solver for Python? I have several challenging non-convex global optimization problems to solve. Currently I use MATLAB's Optimization Toolbox (specifically, fmincon() with algorithm='sqp'), which is quite effective. ... python optimization nonlinear-programming asked by David Ketcheson 78 votes answered by Aron Ahmadia 32 votes ## Can you answer these questions? ### Can Representation Theory be studied computationally / numerically? Can a subfield such as the representation theory of Lie algebras be studied computationally / numerically -- is there an interplay between the abstract and the concrete? I would be grateful for an ... linear-algebra reference-request asked by user33821 1 vote ### evaluating$\coth(x) - 1/x$for real x, on 2 "pieces" The function$\coth(x) - 1/x$has a removable singularity at 0. Its Taylor series is: $$\coth(x) - 1/x = \frac{x}{3} - \frac{x^3}{45} + \frac{2x^5}{945} + \ldots$$ I would like to evaluate the ... numerics asked by Glenn Davis 2 votes ### Hit-n-Run Monte Carlo on convex polytope So, I'm currently trying to implement a MCMC to uniformly sampling hyper-points from the polytope defined as$\mathbb{K}=\{x\in\mathbb{R}^{n}\;\;\text{s.t.}\;\; A\,x=b \}\$ in the specific case where, ...

linear-programming monte-carlo asked by Davide Papapicco 3 votes
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