# Computational Science Stack Exchange 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

### 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

### 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{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

## 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

### 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

### 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

### 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
 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

### 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

### 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 ...

performance