Community Digest

Top new questions this week:

Calculate stable time step DG method for advection-diffusion

For stable time steps for the RKDG method for transport equations we require that $$ \Delta t \le \frac{\Delta x CFL}{(2k + 1)|\lambda|}, $$ where $\lambda$ is the eigenvalue of our conservation law ...

computational-physics numerics discontinuous-galerkin  
asked by Simon 2 votes
answered by ConvexHull 3 votes

Efficient projection of a vector onto matrix kernel

Given an $m \times n$ matrix $A$ and a vector $x\in\mathbb R^n$, with $m<n$, what's an efficient way of computing the projection of $x$ onto the kernel of $A$?

linear-algebra matrix high-dimensional  
asked by becko 2 votes
answered by rchilton1980 5 votes

Surface mesh from labeled 3D points

I'm trying to figure out how to create a surface mesh from a set of labeled 3D points. The 3D object could be something like part of a cave system or asteroid where there would be parts of the surface ...

algorithms computational-geometry mesh-generation  
asked by tapemagnet 1 vote

Linear system with an l1-norm constraint

I have a saddle-point system of the form \begin{equation} \begin{bmatrix} A & B \\ B^T & O \end{bmatrix}\begin{bmatrix} x\\ y \end{bmatrix} = \begin{bmatrix} f \\ \vec{0} \end{bmatrix}, ...

numerics constrained-optimization linear-programming  
asked by VarunShankar 1 vote
answered by Brian Borchers 3 votes

Greatest hits from previous weeks:

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 Christensen 33 votes
answered by Brian Borchers 63 votes

Fastest PCA algorithm for high-dimensional data

I would like to perform a PCA on a dataset composed of approximately 40 000 samples, each sample displaying about 10 000 features. Using Matlab princomp function consistently takes over half an hour ...

high-dimensional data-analysis  
asked by mellow 11 votes
answered by Alexander 11 votes

What is the fastest way to calculate the largest eigenvalue of a general matrix?

EDIT: I am testing if any eigenvalues have a magnitude of one or greater. I need to find the largest absolute eigenvalue of a large sparse, non-symmetric matrix. I have been using R's eigen() ...

linear-algebra algorithms eigensystem sparse-matrix  
asked by power 27 votes
answered by Arnold Neumaier 14 votes

How to solve block tridiagonal matrix using Thomas algorithm

Thomas algorithm can be used to solve a tridiagonal matrix: $$ \begin{bmatrix} {b_ 1} & {c_ 1} & { } & { } & { 0 } \\ {a_ 2} & {b_ 2} & {c_ 2} & { } & { ...

algorithms linear-solver sparse-matrix  
asked by xslittlegrass 6 votes
answered by Shainath 1 vote

Why should non-convexity be a problem in optimization?

I was very surprised when I started to read something about non-convex optimization in general and I saw statements like this: Many practical problems of importance are non-convex, and most ...

optimization nonconvex  
asked by Prokop Hapala 20 votes

Linear interpolation in Fortran

Is there a Fortran subroutine which performs linear interpolation in one-dimenional data? I need something similar to MATLAB function interp1.

fortran interpolation  
asked by kyperros 6 votes

What are some good strategies for improving the serial performance of my code?

I work in computational science, and as a result, I spend a non-trivial amount of my time trying to increase the scientific throughput of many codes, as well as understanding the efficiency of these ...

asked by Aron Ahmadia 66 votes
answered by Pedro 66 votes
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