Computational Science Stack Exchange
Computational Science Stack Exchange

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1500 questions
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Pandas limitations and its alternatives in Python

I read somewhere that Pandas was first developed for the financial world, at least not especially for natural sciences (physics, biology and so on), so is there any similar data analysis Python package more “natural sciences oriented“? I have just…
Clark
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computing the truncated SVD, one singular value/vector at a time

Is there a truncated SVD algorithm that computes the singular values one at a time? My problem: I would like to compute the first $k$ singular values (and singular vectors) of a large dense matrix $M$, but I don't know what an appropriate value of…
SuperElectric
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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: With Hoffman and Kunze with proofs and rigor (I…
Inquest
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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 MATLAB uses the Arnoldi/Lanczos algorithms (for…
Mika Fischer
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How do I plot the surface of a 4D plot?

I am trying to plot the wave function for a particle in a 3D box. This requires me to plot 4 variables: x, y, z axes and the probability density function. The probability density function…
turnip
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11
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Numerical methods for inverting integral transforms?

I'm trying to numerically invert the following integral transform: $$F(y) = \int_{0}^{\infty} y\exp{\left[-\frac{1}{2}(y^2 + x^2)\right]} I_0\left(xy\right)f(x)\;\mathrm{d}x$$ So for a given $F(y)$ I need to approximate $f(x)$ where: $f(x)$ and…
CBowman
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3 answers

Are there finite element software who handles more than five dimensions?

I'm a beginner with FE. My application is the pricing of financial derivatives where the space is five dimensional. So, adding time, the problem has six dimensions. I tried to look around (Fenics, escript, deal.II,...), but my understanding is that…
user729
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4 answers

Learning Fortran

I was wondering what is the best way to learn how to program in Fortran ? I've been looking for books, the examples that seemed OK to me were "Fortran 95/2003 Explained" and "Fortran For Scientists And Engineers". I don't know what you guys think of…
Nick
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10
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How to construct a prolongation and restriction operator for an algebraic multigrid solver?

I am trying to solve a linear system of equations that is sparse, but lacks any kind of banded structure. I have heard that there is a way to extend the principles of a multigrid solver for implicit finite difference schemes to a general linear…
Paul
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Nvidia K20X vs GeForce Titan for GPGPU acceleration

Im trying to understand the difference between these two graphics cards for academic computing, specifically for the DGEMM component. If we look at the raw statistics, both have the same GK110 chip, have comparable statistics in virtually every…
Ophion
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Are there any quad-double arithmetic sparse matrix package?

I am working on some ill-conditioned large sparse linear system of equations. I want to use double-double arithmetic or quad-double arithmetic to solve them. I know that there is a package named MPACK developed by Nakata, Maho, which can perform…
Hanyu Ye
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Confusion about Quantum Monte Carlo

My question is about extracting observables from QMC methods, as described in this reference. I understand the formal derivation of various QMC methods like Path Integral Monte Carlo. However, at the end of the day I'm still confused about on how to…
Pippo
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FAS-multigrid slower than linear defect correction?

I have implemented a V-Cycle multigrid solver using both a linear defect correction (LDC) and full approximation scheme (FAS). My problem is the following: Using LDC the residual is reduced by a factor of ~0.03 per cycle. The FAS implementation does…
Silpion
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What are the differences between Parareal, PITA, and PFASST?

The Parareal, PITA, and PFASST algorithms are all across-the-domain techniques for parallelizing the solution of time-dependent problems in time. What are the guiding principles behind these methods? What are the main differences between them? Can…
eccstartup
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How are the Voronoi Tesselation and Delaunay triangulation problems duals of each other?

I have always been told that the Voronoi diagram is the dual of the Delaunay triangulation problem. In what sense can they be duals of each other? I thought that dual problems (i.e. in linear programming) are supposed to produce the same answer.…
Paul
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