A description of the specific steps needed to solve a particular problem in an unambiguous way, expressed in an abstract form.
23
votes
5answers
703 views
Is algorithmic analysis by flop-counting obsolete?
In my numerical analysis courses, I learned to analyze the efficiency of algorithms by counting the number of floating-point operations (flops) they require, relative to the size of the problem. For ...
19
votes
1answer
274 views
Is there a numerical algorithm for finding an asymptotic slope?
I have a series of data points $(x_i,y_i)$ which I expect to (approximately) follow a function $y(x)$ that asymptotes to a line at large $x$. Essentially, $f(x) \equiv y(x) - (ax + b)$ approaches zero ...
15
votes
5answers
639 views
How can the gravitational n-body problem be solved in parallel?
How can the gravitational n-body problem be solved numerically in parallel?
Is precision-complexity tradeoff possible?
How does precision influence the quality of the model?
13
votes
3answers
219 views
What programming strategies can I take for easily modifying algorithm parameters?
Developing scientific algorithms is a highly iterative process often involving changing lots of parameters that I will want to vary either as part of my experimental design or as part of tweaking ...
13
votes
4answers
607 views
Is Fortuna or Mersenne Twister preferable as an algorithmic RNG?
A recent answer mentioned the use of Fortuna or Mersenne Twister Random Number Generators (RNGs) to seed a Monte Carlo simulation. I hadn't heard of Fortuna before so I looked it up - looks like it is ...
13
votes
2answers
229 views
Is there an efficient algorithm for matrix-valued continued fractions?
Suppose I have a matrix equation recursively defined as
A[n] = inverse([1 - b[n]A[n+1]]) * a[n]
Then the equation for A[1] looks similar to a continued ...
12
votes
4answers
471 views
How do I write dimensionally agnostic code?
I often find myself writing very similar code for one, two, and three dimensional versions of a given operation/algorithm. Maintaining all of these versions can become tedious. Simple code ...
12
votes
3answers
200 views
Uses of power series maps
I'm from the field of accelerator physics, specifically related to circular storage rings for synchrotron light sources. High energy electrons circulate around the ring, guided by magnetic fields. ...
12
votes
1answer
529 views
Algorithms for a many-to-many generalized assignment problem
I can't seem to find any literature on algorithms which can be used to solve a many-to-many generalized assignment problem (GAP), i.e. models where not only can more tasks be assigned to one agent, ...
11
votes
5answers
1k views
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() ...
11
votes
3answers
361 views
Can diagonal plus fixed symmetric linear systems be solved in quadratic time after precomputation?
Is there an $O(n^3+n^2 k)$ method to solve $k$ linear systems of the form $(D_i + A) x_i = b_i$ where $A$ is a fixed SPD matrix and $D_i$ are positive diagonal matrices?
For example, if each $D_i$ is ...
11
votes
1answer
300 views
Enumeration of graphs deriving from Delaunay tessellations in 3D
Is there an algorithm that enumerates the graphs that correspond to some Delaunay tessellation of points in 3D?
If so, is there an efficient parameterization of geometries that correspond to any ...
10
votes
4answers
210 views
What are the benefits and drawbacks inherent to using classes to encapsulate numerical algorithms?
Many algorithms used in scientific computing have a different inherent structure than algorithms commonly considered in less math-intensive forms of software engineering. In particular, individual ...
10
votes
3answers
273 views
Algorithms for (adaptive?) function plotting
I am looking for algorithms to draw standard 2d-graphs for functions that may or may not have singularities. The purpose is to write a "Mini-CAS", so I have no a priori knowledge of the types of ...
9
votes
2answers
395 views
(how to) write simulations that run faster?
I have started using python as the programming language for doing all my assignments in CFD. I have a very little experience in programming. I am from mechanical engineering background and am pursuing ...
