Computational Science Weekly Newsletter - Tuesday, March 31, 2015

Computational Science newsletter

Top new questions this week: How to project a vector into the H(div) space (in the context of finite elements)? Say I have a simple elliptic PDE: $$ -\nabla\cdot(K\nabla p) = f \;\;\;\text{in}\;\Omega $$ with the appropriate boundary conditions. I solve for $p$ using a FEM (a discontinuous Galerkin method to ... pde finite-element discontinuous-galerkin projection   asked by Justin Dong 6 votes answered by Wolfgang Bangerth 2 votes Compute eigenvectors of a matrix with known eigenvalue spectrum If I have already accurately known the eigenvalue spectrum (i.e. all eigenvalues) of a matrix, is there any efficient numerical algorithm to compute all the eigenvectors corresponding to these ... algorithms eigenvalues matrix numerical   asked by Enchantedland 6 votes answered by Jesse Chan 3 votes Why is Matlab's SVD faster on skinny matrices than on fat matrices? I noticed something odd today. I have a matrix X that is very skinny (20800 x 200), double precision real numbers, not sparse, and I want the SVD of it quickly. Matlab does it rather fast: > tic; ... matlab svd   asked by Stephen 3 votes Level 3 BLAS accelerated solver for banded linear systems. At the moment I consider the following problem. I have a huge dense banded matrix $A$ which I want to factorize and use to solve linear systems $Ax=b$. $b$ has around more than 100 columns. At the ... lapack blas   asked by Grisu 3 votes How can calculations cause an arithmetic overflow even if the final value fits? I am reading Algorithm Design Manual by Skiena, which says in Chapter 8, Section 8.1.4 when talking about the calculation of binomial coefficients: Intermediate calculations can easily cause ... algorithms numerical-limitations   asked by Overflow 3 votes answered by Wrzlprmft 11 votes Boundary equations for constant right hand side in Poisson equation (FD) I am setting up to solve a 2D Poisson equation $\nabla^2u = T$ by the finite difference method. I am using the multigrid method. On the coarsest mesh, where the grid size is 2x2, I want to set up ... finite-difference boundary-conditions poisson   asked by PathoNomadic 2 votes Incremental SVD implementation in MATLAB Is there any library/toolbox which has implementation of incremental SVD in MATLAB. I have implemented this paper, it is fast but does not work well. I tried this but in this also error propagates ... linear-algebra matlab svd   asked by p.j 1 vote answered by Geoff Oxberry 4 votes Greatest hits from previous weeks: Do currently available GPUs support double precision floating point arithmetic? I have run the molecular dynamics (MD) code GROMACS on a Ubuntu Linux cluster consisting of nodes containing 24 Intel Xeon CPUs. My particular point of interest turns out to be somewhat sensitive to ... hpc floating-point molecular-dynamics gpu   asked by Andrew 13 votes answered by Godric Seer 14 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   asked by power 18 votes answered by Arnold Neumaier 12 votes Can you answer this? Correctly orthogonalizing and normalizing eigenvectors of a non-hermitian problem I have some non-hermitian matrix $A$, that I have the left and right eigenvectors. (Calculated using SLEPc, by finding the eigenvectors of $A$ and $A^H$). I'm not sure how to orthogonalize them ... eigenvalues non-hermtitian orthogonalization   asked by Andrew Spott 2 votes

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