Algorithms which solve mathematical problems by means of numerical approximation (as opposed to symbolic computation).
2
votes
1answer
38 views
Calculation of elasticity for non-linear curve
I've written this code to calculate the elasticity for econometric analysis. Basically, this algorithm estimate the function:
$$\epsilon(x) = \frac{x}{f(x)}\ f'(x)$$
...
4
votes
1answer
56 views
Generate dictionary of points on n-sphere
This is a long-shot, but my question is to simply optimize this particular function in some code I have written:
...
2
votes
0answers
20 views
Evaluation of e^x with series expansion
My code calculates ex with series expansion. Is there any way to make it shorter and cleaner?
...
5
votes
1answer
105 views
Evaluating a series of Legendre polynomials
The following function represents the electrostatic potential, in spherical coordinates, due to a ring of charge \$q=1\$ and radius \$R=1\$, placed in the plane \$x\$-\$y\$:
$$\phi(r,\theta) = \sum_{...
0
votes
1answer
91 views
Calculate the arclength
I am trying to estimate a good approximation for the arclength of the curve \$ y = \sqrt{1-x^2}\$ for \$x \in [0, 1]\$. I did this using a Bezièr curve, and made it so that the area under the two ...
5
votes
2answers
95 views
Monte Carlo simulation of amoeba population
I wrote a simple Python simulation to answer the "Amoeba" population question posed here:
A population of amoebas starts with 1. After 1 period that amoeba can divide into 1, 2, 3, or 0 (it can ...
2
votes
0answers
46 views
Numerical differentiation using the y-intercept
I have a routine for determining the derivative of a function using the y-intercept (B) to infer the finite difference step (h). ...
4
votes
2answers
125 views
Calculating pi by adding areas of thin rectangles
I wrote a small program for fun to try to prove Pi by taking a certain precision and radius and using it to calculate the area of the circle. My method should be giving me an area that is just ...
5
votes
1answer
95 views
Visualizing Newton-Raphson method for finding zeroes of a function
I have created a program to visualize the working of Newton-Raphson method to find the zeroes of a function:
newton.m:
...
3
votes
2answers
94 views
Implementation of exp function in C using Taylor Series expansion
I am trying to write code to calcultate ex using:
$$e^x = \sum_{n=0}^\infty \frac{x^n}{n!} = 1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \frac{x^4}{4!} + \cdots $$
This is the code I have, which works ...
6
votes
3answers
118 views
1D shock tube problem written in Fortran
I have written a simple Euler solver for the 1D shock tube problem. Eventually, I plan to extend this code to solve the full 3D compressible Navier-Stokes equations. Therefore, I want to start with ...
4
votes
0answers
183 views
Linear Interpolation C++
I have to write a collection of methods for performing linear, bilinear and trilinear interpolation. I have also to write some tests to show that interpolation is exact for polynomials (which should ...
3
votes
1answer
45 views
Square root calculation in Scheme (SICP Exercise 1.7)
I have done exercise 1.7 in SICP (calculate square root precision when change in guesses is under a certain value), but I am calling the change-in-precision function twice in each iteration, which ...
4
votes
2answers
58 views
`atof` revisited
In an answer to this question I mentioned best effort. Here I try to explain what I meant. Please keep in mind that the implementation is intentionally incomplete (missing features such as ...
2
votes
1answer
62 views
Integer square root
This essentially performs the same function as exact-integer-sqrt in math.numeric-tower.
...
3
votes
1answer
48 views
Computing the double Integral using MonteCarlo techniques using Julia
I decided to try and learn Julia for doing scientific computing, and I decided to tackle the problem of finding
$$ \int_{D_{\frac{1}{4}}} x^4 + y^2 dA $$
where \$ D_{\frac{1}{4}} \$ is the part of ...
3
votes
1answer
45 views
Linear shooting method to solve a B.V.P
I have wrote a code to approximate the solution of a boundary value problem:
x'' = p(t)x'(t)+q(t)x(t)+r(t)
x(b) = beta in [a,b]
by using Runge-Kutta method ...
2
votes
1answer
82 views
Double integral solver in TI-84
Here's a program I made for estimating a double integral over a general region. It's pretty accurate, but it's VERY, VERY slow. (Getting an accurate enough result takes about 30 seconds)
Here's the ...
6
votes
1answer
78 views
Approximating π via Monte Carlo simulation
Inspired by a tweet linked to me by a friend and a Haskell implementation by her for the same problem, I decided to try my hand at approximating the value of π using everything in the Haskell standard ...
3
votes
4answers
189 views
Computing integer square roots in Java - follow-up
(See the previous iteration.)
My two previous methods for computing the integer square root of a number \$N\$ ran in the \$\mathcal{O}(\sqrt{N})\$ worst case time. Now I have added a method (...
6
votes
1answer
191 views
Gamma function in Rust
The gamma function is one of a couple nice continuous extensions to the traditional factorial function. I used this Python program as a reference, which in turn, uses this Ada program. As the Ada ...
10
votes
3answers
93 views
Reinventing the Math Functions
Just for practice in the mathematical side of programming, I decided to rewrite the math functions, with the addition of the root() function, which the Math library ...
5
votes
1answer
139 views
Newton's Method Polynomial solver in Ruby
I am learning Ruby programming from "Learn Ruby the Hard way" and I am doing the "Ruby koans".
I have heard a little bit about "Idiomatic" Ruby but I don't know much about it. How can I make it more ...
3
votes
1answer
118 views
Simple neural-network simulation in C++ (Round 4)
You may want to take a look at Rounds 1, 2, and 3, though that isn't necessary for understanding what's below.
The major change since Round 3 is that my code is much cleaner and I'm including ...
3
votes
1answer
104 views
Simple neural-network simulation in C++ (Round 3)
As I mentioned at the end of my Round 2 answer, I've needed to expand my code in order to produce faithfully the data needed for Figure 1 of this paper.
Unfortunately, the updates have made my script ...
3
votes
1answer
145 views
Simple neural-network simulation in C++ (Round 2)
Intro
Yesterday I posted this question. Since then, I've updated my code to incorporate these suggestions. I've also removed the dependence on C++11. Finally, I've made the following changes that ...
4
votes
1answer
314 views
Simple neural-network simulation in C++
The C++ code below simulates the timecourse of the membrane potential (V) of a population of 128 leaky integrate-and-fire ...
2
votes
1answer
68 views
Golden Section Search in Lisp
I implemented the golden section search algorithm recursively in Lisp. My code is:
...
3
votes
0answers
60 views
Decorator for setting up bracketing rootfinding functions
I'm looking for comments on the use of decorators for the following problem (validating initial guesses for bracketing rootfinding methods), as well as any other comments you might have on the design ...
3
votes
3answers
584 views
Implementation of Brent's Algorithm to find roots of a polynomial
I made a program that contains a root-finding algorithm for polynomials as a function and contains 3 test polynomials. The algorithm is Brent's method and is based entirely off the pseudocode from ...
2
votes
2answers
105 views
Root-finding by iterated bisection
Both of the following code give the same result. But I'm not sure where should I put the raise statement.
...
2
votes
0answers
25 views
Iterative procedure to get 3D coordinates from distance constraints
Imagine you have a series of n points randomly generated in a box in 3D space. You also have a list of distance bounds, e.g. points 5 and 3 should be between 1.0 and 2.0 Angstroms apart.
There are ...
8
votes
4answers
230 views
Buffon's Needle experiment
I was working on a program that simulates the Buffon's Needle experiment. If anyone is not familiar with it, a Wiki link is provided - Buffons's Needle
The point of Buffon's experiment is to find ...
7
votes
1answer
105 views
Monte Carlo Pi (MASM)
I'm currently trying to brush up on my assembly skills and, being at the FPU section of the tutorial, I implemented a very basic version of a Monte-Carlo-Algorithm to compute pi. I deliberately use ...
2
votes
3answers
89 views
Calculating e^x by math.h and by own means
For this program, the user needs to enter an exponent and the program will calculate \$e\$ (Euler's number) to the power of the exponent the user inputs.
This is done by two ways:
By the math.h ...
2
votes
1answer
66 views
Utility Method to find the Square root of a number
Utility to calculate the square root of a number. The method also accept an epsilon value, which controls the precision. The epsilon value could range to any number including zero. I am expecting a ...
4
votes
1answer
306 views
Poker Odds Calculation with Monte Carlo
I have created an Odds Calculator in Java. The program gives me the odds, but I want to make sure that they are correct. Maybe someone can tell me a calculator I can compare my results with or knows ...
1
vote
2answers
131 views
3
votes
0answers
83 views
Terry Feagin's 10th order explicit Runge-Kutta method
The following Julia code implements Terry Feagin's 10th order explicit Runge-Kutta method (a more accurate cousin of RK4). Though the structure of the code is quite simple (i.e. no cyclomatic ...
0
votes
1answer
99 views
Summation for π [closed]
I was going through my Java book's exercise solutions and comparing and incorporating the author's techniques into my repertoire.
Most of the time, my approach is identical to the author's. When it ...
5
votes
1answer
359 views
Iterative equation solver in Python
In order to solve a equation where the left hand side appears under an integral on the right hand side:
$$
B(p^2) = C\int_0^{p^2}f_1\left(B(q^2),q^2\right)\mathrm{d}q^2 + C\int_{p^2}^{\Lambda^2} f_2\...
1
vote
2answers
236 views
Bisection method for finding the root of a function
For those who aren't familiar with the bisection method for finding the root of a function (i.e. finding where \$f(x) = 0\$) the basic idea is:
Take a function \$f(x)\$ and an interval \$[a,b]\$
If \...
3
votes
1answer
111 views
Comparing multiple arguments and returns the smallest argument
I want to see if anyone knows how to optimize the code below:
...
4
votes
2answers
2k views
Square Root Calculator
I have now written a simple square root calculator using the division method:
...
3
votes
0answers
65 views
Volatility updating with Heston-Nandi model
I'm trying to program a volatility updating rule using iteration. I start with the well-known Heston-Nandi model where the returns dynamics are:
$$
\left\{
\begin{array}{rcl}
R_{t+1} &=&...
2
votes
2answers
136 views
Newton's square root
This is the code I wrote to compute the newton's square root of a number.
I aimed for extreme clarity over efficiency and I have put an abundant docstring at the start of the ...
14
votes
2answers
781 views
Pi by Monte-Carlo
I was inspired by this SO post to investigate
a good Java8 way to calculate Pi based on simulation.
I used a similar task to learn about parallel programming on both CUDA,
and Intel Xeon Phi ...
3
votes
2answers
115 views
Multifunctional Monty Hall Simulator
Based on this question on math.SE regarding probabilities in variations on the Monty Hall problem, I cobbled up a simulator in Ruby to give myself an introduction to the language.
Since this is my ...
3
votes
1answer
275 views
Percentage based drop prize on Mob entity kill
I have created a simple percentage-based random prize drop for killing certain mobs.
A drop is basically what the player will get in return for killing a mob, as a reward.
So I have a large list of ...
15
votes
6answers
8k views
Monte Carlo pi calculation
In order to learn the basics of Monte Carlo I calculated pi with it.
I also wrote an explanation of the reasoning behind the code.
Down here you can see the circle with random points that I simulated ...
