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1500 questions
7
votes
1 answer
Shall I derandomize a randomized algorithm in real application?
In general (and in real application), suppose I am using a randomized algorithm (e.g. Use MCMC to sample from a distribution and then compute $E(f(x))$ for some function $f$)
Assume my algorithm will face every possible input and I use a…
wh0
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7
votes
3 answers
Algorithm to compare two large sets
I am a novice in the world of algorithms, ignorant of the taxonomy used.Please pardon me.
I have two large sets of numbers A and B where A = {x| 0< x< 9999999999 } B= {y | 0 < y < 9999999999 }. The cardinality of these sets is more than a million.…
user917279
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7
votes
2 answers
What are some of the differences between using a Lagrangian and Eulerian framework to quantify passive scalar dynamics?
On one hand, one may seed the domain with particles and track their trajectories in the Lagrangian sense by implementing a Lagrangian particle tracking model. On the other hand, one may use the Eulerian approach and solve a scalar transport…
Isopycnal Oscillation
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7
votes
2 answers
What is the difference between Coupled Cluster SD and SD(T)?
Can you explain the difference between these two computational methods ?
Stefano Borini
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6
votes
4 answers
Approximately "solving" a linear system of equations without a feasible solution
A linear system of equations has the form $Ax = b$, where a matrix $A$ and a
vector $b$ are given, and I wish to find a solution vector $x$.
Suppose that the system $Ax = b$ has no feasible solution. Then I
wish to find a solution vector $x$ such…
sara
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6
votes
3 answers
Newton's method for a given polynomial
Let $f(x)=\frac{1}{5}x^5+\frac{1}{3}x^3+x-1$
Show that $f$ has only one zero $r$ in interval $(0,1)$
To find approximation of $r$ we apply Newton's method $x_{n+1}=x_n-\frac{f(x_n)}{f'(x_n)}$. Show that for every $x_0\in(0,1)$ this method…
xan
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6
votes
3 answers
Fast algorithm for Polar Decomposition
As it known, according to the Polar Decomposition, square matrix can be expressed in the next form $$M=QR$$ ($Q$ - orthogonal matrix $R$ - positive-semidefinite Hermitian matrix)
I need to find this $Q$ factor for the case of $3\times 3$ matrix.…
Stepan Loginov
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6
votes
5 answers
Using multiple languages in scientific codes
Short version: Is it ever a good idea to use multiple languages in scientific codes?
Long version: May be its just me but these days I often see scientific codes written in multiple languages. The argument is that one language is used for…
stali
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6
votes
2 answers
Determine the step size in a differential equation numerical solver
How can we define the precision we require in a numerical differential equation solver? What is it that I have to optimize to know? And how do I know that I'm at a sufficient time-step value?
For example, in those programs like Mathematica and…
The Quantum Physicist
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6
votes
2 answers
Big matrix multiplication on single machine
For example I have 2 matrices that can't fit in RAM.
I need algorithm or library which can handle this.Preferably Matlab or Python.
I think it can be some block matrix multiplication? Also I think there is an analogy hard drive<->ram, gpu ram<->cpu…
mrgloom
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6
votes
2 answers
How important is the exponential of a matrix in computational science?
CS people:
The title is the question, as I will explain. As everyone reading this probably knows, if $A$ is a square matrix of real or complex numbers, then $e^A$, or $\exp(A)$, is the matrix of the same dimensions as $A$ defined by the obvious…
Stefan Smith
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6
votes
2 answers
Does the finite element method impose any restrictions on the Peclet number for numerical stability?
Background on finite volume method
When discretising the flux with a central difference stencil of the the advection-diffusion equation restriction $\frac{ah}{d} < 2$ must be observed for the finite volume method to remain numerical stability. Where…
boyfarrell
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6
votes
3 answers
How to sample numerically from an arbitrary smooth distribution?
I'm given a smooth probability density function via its values on a reasonable fine grid. I assume that cubic spline interpolation (or cubic spline interpolation of the logarithm of the density) will be sufficient to evaluate it at arbitrary points…
Thomas Klimpel
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6
votes
3 answers
Preconditioner for finding the smallest eigenpairs of a large, but structured, matrix
I'm trying to find the eigenvector corresponding to the second smallest eigenvalue of a large $(4,000,000 \times 4,000,000)$ matrix $L$. $L$ is a graph Laplacian, with the following structure: $L = D - SBS^\intercal$, where $D$ is a diagonal matrix…
Jeff
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6
votes
2 answers
Numerical instability of spherical pendulum
Problem statement
I am trying to simulate a spherical pendulum, with
rod length $r$
south-polar angle $\theta$ and azimuthal angle $\phi$
initial values $(\theta_0,\phi_0)= (0,0)$
My particular pendulum is hanging in a construction, which can be…
Rody Oldenhuis
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