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1500 questions
11
votes
4 answers
Maximizing a convex function (minimizing a concave function) with a linear constraint
The problem is
$$\max f(\mathbf{x}) \text{ subject to } \mathbf{Ax} = \mathbf{b}$$
where $f(\mathbf{x}) = \sum_{i=1}^N\sqrt{1+\frac{x_i^4}{(\sum_{i=1}^{N}x_i^2)^2}}$,
$\mathbf{x} = [x_1,x_2,...,x_N]^T \in \mathbb{R}^{N\times 1}$, and
$\mathbf{A}…
Sooraj
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11
votes
1 answer
Statistical models for local memory/compute, network latency, and bandwidth jitter in HPC
Parallel computation is frequently modeled using a deterministic local rate of computation, latency overhead, and network bandwidth. In reality, these are spatially variable and non-deterministic. Studies such as Skinner and Kramer (2005) observe…
Jed Brown
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11
votes
4 answers
Calculating determinant while solving $Ax=b$ using CG
I am solving $Ax=b$ for a huge sparse positive definite matrix $A$ using the conjugate gradient (CG) method. It is possible to compute the determinant of $A$ using the information produced during the solve?
Manuel Schmidt
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11
votes
3 answers
I am looking for a parallel dynamic graph library in C++
Hello scicomp community,
I have worked in the area of graph algorithms using frameworks such as NetworkX (Python), JUNG and YFiles (Java). I am now entering the area of parallel and high perfomance computing. For a new project, I am looking for a…
clstaudt
- 243
- 2
- 10
11
votes
3 answers
Regression testing of chaotic numerical models
When we have a numerical model that represents a real physical system, and that exhibits chaos (e.g. fluid dynamics models, climate models), how can we know that the model is performing as it should? We cannot compare two sets of model output…
naught101
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11
votes
1 answer
Is using iterative methods to solve a linear system always superior to inversing the matrix?
I have a silly question. Is it always more computationally efficient to use iterative methods to solve for some matrix $A$, $Ax=b$, where $x$ and $b$ change but $A$ stays constant, compared to computing the inverse $A^{-1}$?
The rationale for…
Touko Puro
- 131
- 4
11
votes
2 answers
What makes a good preconditioner when only a few approximate iterations are needed?
For deterministic solver of $Xw=y$, one recommendation is to pick $P$ such that $P^{-1}X$ has a low condition number. However, this condition only really matters when you want to reduce initial error a lot, ie, by a factor of $10^{-15}$. There are…
Yaroslav Bulatov
- 2,655
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11
votes
2 answers
Why is RK45 used as the "default" method for non-stiff ODEs rather than a multistep one?
From what I read, the "default" go-to method for non-stiff ODEs is the Dormand-Prince Runge-Kutta pair; for instance, in Matlab docs, "Most of the time, ode45 should be the first solver you try".
However, from what I understand multistep methods…
Federico Poloni
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11
votes
4 answers
What can a computational scientist do in the fourth industrial revolution?
This question is neither scientific nor technical but more career related.
I am at a junction in my professional life where I need to make a decision with regard to the future of my career. At the moment I am an R&D manager and my job is very…
Dude
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11
votes
1 answer
How to compute Singular value decomposition of a large matrix with Python
Language: Python3
Problem: I have a matrix Q of shape [51200 rows x 51200 cols] stored in a binary file, each of the element in this matrix has a data type of complex64. To load the data into memory I therefore need ~20GB of RAM, checked from…
SAM
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11
votes
1 answer
Are there Improved ways of computing $p \log(p)$?
Most math libraries have a number of versions of logarithm functions.
Most of the time we assume them to be perfect, but actually quite a lot of them just offer a certain number of digits of precision.
For some functions, there are numerically more…
Has QUIT--Anony-Mousse
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11
votes
5 answers
Increasing the archival longevity of code
Is there a published list of best practices to ensure longevity of code, with an eye towards reproducible scientific results? (e.g. open source, documentation practices, selecting dependencies, selecting a language, virtual machines, etc).
Know of…
cboettig
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11
votes
3 answers
How much more work is it to code math models in Python, compared to working with Matlab?
If one had to code up a new dynamical system for a research group at a university, and the university has a Matlab total headcount license so that one could code in Matlab, are there any benefits to coding in Python instead? How much more work…
user33708
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11
votes
1 answer
Implications of thermodynamic inconsistency in CFD calculations
During my PhD work, I had to use tabulated values of thermodynamic properties of gases in some Computational Fluid Dynamics (CFD in short) simulations.
My tables are discretized in temperature and pressure (which are the independent variables) as…
iterrate
- 111
- 4
11
votes
3 answers
Relative comparison of floating point numbers
I have a numerical function f(x, y) returning a double floating point number that implements some formula and I want to check that it is correct against analytic expressions for all combination of the parameters x and y that I am interested in. What…
Ondřej Čertík
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